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Statistics - Class 11 Engineering Maths - Extra Questions

Find the median of the following data: 2,7,3,15,12,17 and 5.



Find the mode of 14,25,14,28,18,17,18,14,23,22,14,18.



Calculate the coefficient of range for the following data:
Heights in cm.120124125129130134135139140144
No. of students6910128



Calculate the coefficient of range for the following data.
No. of wards12345678
No. of houses32572896138906658



Calculate the mean deviation from the mean for the scores given below:
15,11,13,20,26,18,21



The formula for coefficient of variation (C.V.) is given by _______________.



The weight(in kg) of 13 students in a class are 42.5,47.5,48.6,50.5,49,46.2,49.8,45.8,43.2,48,44.7,46.9,42.4. Find the range and coefficient of range.



The smallest value of a collection of data is 12 and the range is 59. Find the largest value of the collection of data.



Write two merits of mode.



The largest value in a collection of data is 7.44. If the range is 2.26, then find the smallest value in the collection.



Find the mode of the following data. 12, 24, 36, 46, 25, 38, 72, 36, 25, 38, 12, 24, 46,25, 12, 24, 46, 25, 72, 12, 24, 36,25, 38 and 36.



Write the relation between standard deviation of a set of scores and its variance.



What is the range of the data : 48, 65, 27, 23, 44, 41, 25, 70, 49 ?



Find the mean S.D of 1,2,3,4,5,6



Find the sum of deviation of all observations of the data 5, 8, 10, 15, 22 from their mean.



Find the mode of this data
2,5,4,3,5,2,5,2,4,5



The rainfall ( in mm) in a city on 7 days of a certain week was recorded as follows:


Days



Mon



Tue



Wed



Thurs



Fri



Sat



Sun



Rainfall


( in mm)



0.0



12.2



2.1



0.0



20.5



5.5



1.0




 i) Find the range of the rainfall in the above data.




The runs scored in a cricket match by 11 players is as follows:
6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Find the mean, mode and median of this data. Are the three same?



Calculate the variance and standard deviation of the following continuous frequency distribution
Class interval 30-4040-5050-6060-7070-8080-9090-100
Frequency 371215832



Find the standard deviation of 9,16,23,30,37,44,51.



Find the median of:
26, 33, 41, 18, 30, 22, 36, 45 and 24



The S. D of 15 items is 6 and if each item is decreased by 1 , then standard deviation will be



Find the median of:
3.2, 4.8, 5.6, 7.3, 8.9 and 9.1



Let a, b, c, d and e be the observations with mean { m } and standard deviation s. The standard deviation of the observations a +  { k } , b+k ,c+k , d+k and e+k is



Find the median of:
80, 48, 66, 61, 75, 52, 45 and 70



Find the coefficient of range for the following data.
Size10-1515-2020-2525-30
Frequency2468



Following tare the lives in hours of 15 pieces of the components of aircraft engine. Find the median: 715,724,725,710,729,745,694,699,696,712,734,728,716,705,719



Find the median of 8, 15, 7, 19, 16, 12 and 10



What is mode ?



If the median of \cfrac{a}{3},\cfrac{a}{2},\cfrac{a}{4},\cfrac{{2a}}{5},\cfrac{a}{6} is 12 then find the value of a\left( {a > 0} \right).



The median of the given data 6,8,9,15,x,29,25,21,22 is 18, find value of x ?



Calculate variance and standard deviation of the following data :
10, 12, 8, 14, 16



Find the median of the following :
33,31,48,45,41,92,78,51,61



A die is tossed thrice. Getting an even number is considered as success. What is the variance of the binomial distribution ?



Find the mean deviation from the mean of the following data, using the step deviation method:
MarksNo. of students
0-106
10-205
20-308
30-4015
40-507
50-606
60-703



From the following frequency distribution, find :
(i) the median
(ii) lower quartile
(iii) upper quartile
(iv) inter quartile range

Variate

15

18

20

22

25

27

30

Frequency

4

6

8

9

7

8

6



A data has 13 observations arranged in descending order. Which observation represents the median of data?



The distribution below gives weights of 30 students of a class. Find the median weight of the students.



The length of 40 leaves of a plant are measured correctly of the nearest millimeter, and the data obtained is represented in the following table:
Find the median length of the leaves.



The average weight of 40 Students is 32. If the Heaviest and Lightest are excluded the average weight reduces by 1. If only the Heaviest is excluded then the average is 31. Then what is the weight of the Lightest?



The exam scores of all 500 students were recorded and it was determined that these scores were normally distributed. If Jane's score is 0.8 standard deviation above the mean, then how many, to the nearest unit, students scored above Jane?





25, 16, 26, 16, 32, 31, 19, 28 and 35



Find the mode of the following distribution:
Income (in rupees)500-600400-500300-400200-300100-200
Number of persons1720301815



Find the mode of the following data:
Marks below1020304050
Number of students38172022



Find the mode of the following distribution:
Marks more than01020304050
Number of students50464020103



Find the mode of the following distribution:
Marks45678910
Frequency 381012161210



Find the mode of the following distribution:
Age in (years)0-1010-2020-3030-4040-5050-6060-70
Frequency 814252825105



Find the mode of the following data:
Class interval1112131415161718
Frequency29348783



Find the median of
3.2,4.8,5.6,5.6,7.3,8.9 and 91



The marks (out of 100) obtained by 7 students in Mathematics examination are given below. Find the mode for these marks.
99, 100, 95, 100, 100, 60, 90



2.5 2.5 2.1 2.5 2.7 2.8 2.5



2 4 6 2 6 6 7 8



Find the mode of the following data.

Marks353637383940
No of Student 090709040402



Find mode of the following frequency distribution :
x345678
f246321



A data has 19 observations arranged in descending order which observation represents the median data?



Find mode of the following frequency distribution :
x1.11.21.31.41.51.6
f20508060158



2  5 7  5 3  1  5 8 7  5



The weights of 10 students (in kg) are given below :
40, 35, 42, 43, 37, 35, 37, 37, 42, 37
Find the mode of the data.



The number of members in 30 families of a village are according to following table.
Find their mode.
No. of members2345678
No. of families12461035



Marks obtained by students are given below, find the mode of marks.
Marks1020304050607080
No. of Students281626201674



Age in years of 20 students of a class are as follows:
15    16    13    14    14
13    15    14    13    13
14    12    15    14    16
13    14    14    13    15
Find mode by expressing them in frequency distribution:



Find the median of :
66, 98, 54, 92, 87, 63, 72



Find mode of the following frequency distribution
MarksNo. of Students
0 - 105
10 - 2012
20 - 3014
30 - 4010
40 - 508
50 - 606



Find the mode of 0, 5, 2, 7, 2, 1, 1, 3, 2, 4, 5, 7, 5, 1 and 2 



Find the mean and variance for the data 6, 7, 10 , 12, 13, 4, 8, 12



Find the mean and variance for the data
  \displaystyle X_{i} 6101418242830
\displaystyle f_{i}
24712843



Find the mean deviation about the mean for the data 
4, 7, 8, 9, 10, 12, 13, 17



Find the mean and standard deviation using short-cut method
  \displaystyle X_{i}   606162636465666768
  \displaystyle f_{i}   21122925121045



Find the mean and variance for the following frequency distrubution
Classes0-1010-2020-3030-4040-50
Frequencies5815166



Find the mean and variance for the following frequency distribution 
Classes0-3030-6060-9090-120120-150150-180180-210
Frequencies23510352



Find the mean deviation about the mean for the data 
38, 70, 48, 40, 42, 55, 63, 46, 54, 44



Find the mean and variance for the data
  \displaystyle X_{i} 92939798102104109
\displaystyle f_{i}
3232633



Find the mean variance and standard deviation using short-cut method
Height
in cms
No. of children
70-753
75-804
80-857
85-907
90-9515
95-1009
100-1056
105-1106
110-1153



Find the mean deviation about the median for the data 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17.



The sum and sum of squares corresponding to length X (in cm ) and weight y
 (in gm) of 50 plant products are given below:
  \displaystyle \sum_{i=l}^{50}X_{i}=212, \sum_{i=l}^{50} X_{i}^{2}=902.8, \sum_{i=l}^{50}y_{i}=261,\sum_{i=l}^{50}y_{i}^{2}=1457.6  
Which is more varying  the length or weight ?



The mean and variance of eight observation are 9 and 9.25, respectively. If six of the observation are 6, 7, 10, 12, 12 and 13, find the remaining two observations.



The mean and standard deviation of marks obtained by 50 students of a class in three
subjects Mathematics, Physics and chemistry are given below :
SubjectMathematicsPhysicsChemistry
Mean423240.9
Standard deviation 121520
Which of the three subjects shows the highest variability in marks and which shows the
lowest ?



The mean and standard deviation of a group of 100 observations were found to be 20 and 3 respectively. Later on it was found that three observations were incorrect which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observation are omitted 



From the data given below state which group is more variable A or B 
Marks10-2020-3030-4040-5050-6060-7070-80
Group A917323340109
Group B1020302543157



The diameters of circles (in mm) drawn in a design are given below :
Diameters No. of circles
33-3615
37-4017
41-4421
45-4822
49-5225



Given that  \displaystyle \bar{X} is the mean and  \displaystyle \sigma ^{2} is the variance of  \displaystyle n  observations  \displaystyle X_{1},X_{2}...X_{n }  . Prove that the mean and variance of the observations  \displaystyle aX_{1},aX_{2},aX_{3}....aX_{n }   are  \displaystyle \bar{ax}   and  \displaystyle a^{2}\sigma ^{2}   respectively  \displaystyle (a\neq 0)  .



From the prices of shares X and Y below find out which is more stable in value :
X35545253565852505149
Y108107105105106107104103104101



The mean and standard deviation of 20 observation are found to be 10 and 2 respectively. On rechecking it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases :
(i) If wrong item is omitted
(ii) If it is replaced by 12



The mean and standard deviation of six observation are 8 and 4 respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.



The following number of goals were scored by a team in a series of 10 matches:
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Find the mean, median and mode of these scores.



The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x+2, 72, 78, 84, 95



Write the marks wise frequencies in the following frequency distribution table.
MarksUp to 5Up to 6Up to 7$Up to 8Up to 9Up to 10
No of students51119314045



Find the mean deviation about mean for the following data:
14, 21, 28, 21, 18



The relative humidity (in %) of a certain city for a September month of 30 days was as follows:
98.198.699.290.386.595.392.996.394.295.1
89.292.397.193.592.795.197.293.395.297.3
96.092.184.990.095.798.397.396.192.189
What is the range of the data?



The marks scored by 60 students in a science test are given below.
Marks (x)102030405060
No. of students (f)812201073
Calculate the variance and standard deviation



Calculate the range and coefficient of range from the following data:
Number of trees planted in 6 months: 186, 234, 465, 361, 290, 142



The number of books bought by 200 students in a book exhibition is given below.
No. of books01234
No. of students3564681815
Find the variance and standard variation



Find the mean deviation about median for the following data.
18, 23, 9, 11, 26, 4, 14, 21



The daily wages of 40 workers of a factory are given in the following table.
Wages in Rs30-3434-3838-4242-4646-5050-54
No. of workers4791163
Calculate i) Mean (ii) Variance and (iii) Standard deviation of wages and interpret the findings



Calculate the range and coefficient of range from the following data:
Marks scored by 12 students in a test: 31, 18, 27, 19, 25, 28, 49, 14, 41, 22, 33, 13



Find the mean deviation about mean for the following data.
15, 18, 13, 16, 12, 24, 10, 20



If 'x' varies inversely as 'y' and x=7 when y=9:
(a) Find constant of variation (k).
(b) Write equation of variation.
(c) Find 'y' when x=9.



The coefficient of range of the data set \{3,1,4,2,5,9,8\} can be represented as \dfrac{p}{q} where p and q are co-primes. Then the value of (q-p)^2 is:



Find the range and the coefficient of range of 43, 24, 38, 56, 22, 39, 45



Find the range and the coefficient of range of 43, 24, 38, 56, 22, 39, 45



Find the mean deviation about the median for the following data.
13, 17, 16, 11, 13, 10, 16, 11, 18, 12, 17



Find the standard deviation of the first 10 natural numbers.



Calculate the Standard Deviation and coefficient of variation for the given frequency table:
Class-interval    Frequency
1-51
6-102
11-153
16-204



Find the variance for an ungrouped data 5, 12, 3, 18, 6, 8, 2, 10.



Calculate variance for the following data: 2,4,6,8 and 10.



Find standard deviation 50, 56, 59, 60, 63, 67, 68.



The p.m.f. of a r.v. X is
P(x) = \left\{\begin{matrix}\dfrac {2x}{n(n + 1)}, & x = 1, 2, ... n;\\ 0, & otherwise.\end{matrix}\right.
Find E(X) and Var (X)



Compute standard deviation for the following data.
Class:0-44-88-1212-1616-20
Frequency:61012108



If the mean of the data: 7, 8, 9, 7, 8, 7, \lambda, 8 is 8, then the variance of this data is?



In binomial distribution, the sum and the product of mean and the variance are \dfrac{25}{3} and \dfrac{50}{3} respectively. Determine the distribution.



Obtain the mean and standard deviation for the following data set:
X10203040506070
Y05153035252708



Write the formula of mode for grouped data and explain terms in it.



Given N = 10 , \Sigma x_i = 60 and \Sigma x_i^2= 1000 . The standard deviation is



The following table given the daily wages of workers in a factory. Compute the standard deviation and the coefficient of variation of the wages of the workers.
Wages (Rs)125-175175-225225-275275-325325-375375-425425-475475-525
Number of workers22219143461



If a coin is tossed three times and X= number of heads, then find E(X) and V(X).



The ages of ten students of a group are given below. The ages have been recorded in years and months:
8-6,9-0,8-4,9-3,7-8,8-11,8-7,9-2,7-10,8-8
What is the lowest age?
What is the highest age?
Determine the range?



Find the expected value, variance and standard deviation of a random variable whose p.m.f is.
X=x123
p(X=x)\frac{1}{5}\frac{2}{5}\frac{2}{5}



On situation where mode would be an appropriate representative value.



The variance of first 50 even natural numbers is



Find the mode of 10 observations, if their mean is 5 and median is 4.



Find the median of:
17, 23, 36, 12, 18, 23, 40 and 20.



The mean deviation from mean of the observation a,a+d,a+2d,....,a+2nd is



Calculate the range and coefficient of range with following data
Marks0-1010-2020-3030-4040-50
No. of student 0205070803



Find the mean deviation from the median for the following data:
x_1^{}
6931215132122
f_1^{}45325443



Determine (a) the mode (b) the median , and (c) the mean for each of the following set of data :
(i) 1,16,11,6,11,8,14,11,21



Find the standard deviation of 10 observations 111,\ 211,\ 311,...,1011



The smallest and largest numbers in the data are 21 and 60 respectively. Find the range of the data.



Define both of these:- median, altitude 



Find the mean deviation about the median for the data 
36,72,46,42,60,45,53,46,51,49



A random variable X has the following probability distribution.
X=x-2-10123
P(X=x)0.1k0.22k0.3k
Find the value of k and the variance of X.



Find the mean deviation about the median for the data 
13,17,16,14,11,13,10,16,11,18,12,17



In a traffic survey of 125 cars, the number of people in each car was recorded.
Number of people in each car12345
Frequency504010205
Find the range. 



Make a frequency table each of the following sets of data.
(i) Ages of students in years in class VI B of a school:
12,13,13,14,14,14,14,13,13,14,13,14,13,13,12,14,13,14,12,13
(ii) The median used by students of class VI B of a school to listen to music:



If the mean is 54 and mode 52, find the median. 



On the annual day of school age-wise participation of students is given in the following frequency distribution table. Find the median of the students
1363530_c34b713e6e344d71adcbb192f74c5da2.png



Find the median of variants 5, 7, 8, 11, 13, 17 with frequencies 3, 7, 7, 12, 13, 10 respectively.



Find the median of the following data:
3, 1, 5, 6, 3, 4, 5



Find the median of the following data:
3, 1, 5, 6, 3, 4, 5, 6



The mean and standard deviation of 50 items were found to be 75 and 10 respectively. At the time of checking it was found that one item 65 was incorrect. Calculate the mean and standard deviation, if the wrong item is omitted.



Write the first 10 prime numbers and find their median.



Is the mode always at the center of data?



The median of 43,75,15,86,30 is 



Find the median of the observations:59, 75, 68, 70, 74, 75, 80.



Find the mean deviation about the mean for the data:
4,7,8,9,10,12,13,17



Find the median
61-705
81-8015
81-9020
91-10030
101-11010
111-1208



More than ogive and less than ogive for a given data with mean 23 meet at (20,22). find its mode.



The marks obtained by 11 students of a class in a test are given below:-
    23,2,15,38,21,19,23,23,26,34,23
Find the mode of the above data.



Find the mode for the following data:
7.5, 7.3, 7.2, 7.2, 7.4, 7.7, 7.7, 7.5, 7.3, 7.2, 7.6, 7.2



Find the mean, variance and standard deviation for first six odd natural numbers. 



Find the median of:
3, 11, 7, 2, 5, 9, 9, 2, 10



Using short ad method.find the mean, variance and standard deviation for the data: 
Class30-4040-5050-6060-7070-8080-9090-100
Frequency371215832



Find the median of:
21, 15, 6, 25, 18, 13, 20, 9, 16, 8, 22



Find the mean, variance and standard deviation for the numbers 4, 6, 10, 12, 7, 8, 13, 12.



Find the median of:
10, 32, 17, 19, 21, 22, 9, 35



Using short ad method.find the man, variance and standard deviation for the data: 
x_i6101418242830
f_i24712843



Using short ad method.find the man, variance and standard deviation for the data: 
x_i481117202432
f_i3595431



Find the median of first 15 odd numbers.



The age (in years) of 11 cricket players are given below:
28, 34, 32, 41, 36, 32, 32, 38, 32, 40, 31
Find the mode of the ages.



Find the median for the following distribution:

 Wages per day in Rs. 3845  4855  62 65
 No. of workers 14 8 7 10 6 2




For the following set of numbers, find the median: 10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9, 15.



Find the median of first 50 whole numbers.



A student scored the following marks in 11 questions of a question paper: 3, 4, 7, 2, 5, 6, 1, 8, 2, 5, 7 Find the median marks.



Find the median of:
55, 60, 35, 51, 29, 63, 72, 91, 85, 82



Find the mode of the data:
27, 23, 39, 18, 27, 21, 27, 27, 40, 36, 27



Find the mode of the data:
10, 8, 4, 7, 8, 11, 15, 8, 6, 8



Find the median of the following set of numbers: 9, 0, 2, 8, 5, 3, 5, 4, 1, 5, 2, 7.



At a shooting competition, the scores of a competitor were as given below :

Score

0

1

2

3

4

5

No. of shots

0

3

6

4

7

5

What was his median score?



Marks obtained by 70 students are given below:

Marks

20

70

50

60

75

90

40

No. of students

8

12

18

6

9

5

12

Calculate the median marks.



Find the mode of the following observations
5, 7, 6, 8, 9, 0, 6, 8, 1, 8



Find the mode of the following sets of numbers:3, 2, 0, 1, 2, 3, 5, 3.



 Find the median for the following distribution.

Marks

35

45

50

64

70

72

No. of students

3

5

8

10

5

5



The daily wages in (rupees of) 19 workers are

41, 21, 38, 27, 31, 45, 23, 26, 29, 30, 28, 25, 35, 42, 47, 53, 29, 31, 35.

Find the median?



A boy scored the following marks in various class tests during a term each test being marked out of 20: 15, 17, 16, 7, 10, 12, 14, 16, 19, 12, 16. What are his median marks?



Find the mode of the following sets of numbers: 9, 0, 2, 8, 5, 3, 5, 4, 1, 5, 2, 7



Find the median of first nine even natural numbers.



Find the
mean deviation about the median for the data

x_i579101215
f_i862226



Enter 1 if it is true else enter 0.
In a set of observations, the observation that occurs the most often is called Mode.



Enter 1 if it is true else enter 0.
In a given data, arranged in ascending or descending order, the middle most observation is called Median.



Observe the data and answer the questions that follow:
16,15,16,16,8,15,17
(a) Which data value can be put in the data so that the mode remains the same?
(b) At least how many and which value(s) must be put in to change the mode to 15?
(c) What is the least number of data values that must be put in to change the mode to 17? Name them.



Enter 1 if it is true else enter 0.
Mean, Median, Mode are the measures of Central tendency.



Find the mean deviation about the mean for the data. 

x 510152025
f_{i} 74635



Find the mode of the given data:
10,8,4,7,8,11,15,8,4,2,3,6,8



Age (in years) of 6 children of two groups are recorded as below:
          Group A                        Group B         
               7                    7
               7                    9
               9                    11
               8                    12
              10                   12
              10                   12

(a) Find the mode and range for each group.
(b) Find the range and mode if the two groups are combined together



Find the median of
26,33,41,18,30,22,36,45, and 24



Find the mean deviation about the median for the data

\mathrm{x_i} 1521273035
\mathrm{f}_{\mathrm{i}}35678



A student got the following marks in 9 questions of a question paper.
3, 5, 7, 3, 8, 0, 1, 4 and 6.
Find the median of these marks.



Find the mean and variance for the data
x_i6101418242830
f_i24712843



Find the mean and variance for the data
x_i92939798102104109
f_i3232633



Find the mean and variance for the first n natural numbers 



Find the mean and the median of :
2,4,5,8,10,13 and 14



Find the mode of the following distribution:
Marks0-1010-2020-3030-4040-5050-6060-7070-80
Number of students1520242412317152



Fill in the blanks:
A data arranged in ascending or descending order is called an........ data.



Find the mode of the following data: 9, 11, 8, 11, 16, 9, 11, 5, 3, 11, 17 and 8



From the following data, find: Median
25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38 and 83



The marks obtained by 19 students of a class are given below:
27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35 and 28. Find: median 



The following table shows the expenditure of 60 boys on books. Find the mode of their expenditure:
1834252_ee07b36a0c014bdd802ecdcecc1cf16a.PNG



241, 243, 347, 350, 327, 299, 261, 292, 271, 258 and 257.



63, 17, 50, 9, 25, 43, 21, 50, 14 and 34.



Find the mode of the following data: 7, 9, 8, 7, 7, 6, 8, 10, 7 and 6.



Out of 10 students, who appeared in a test, three secured less than 30 marks and 3 secured more than 75 marks. The marks secured by the remaining 4 students are 35, 48, 66 andFind the median score of the whole group.



233, 173, 189, 208, 194, 204, 194, 185, 200 and 220.



The weights (in kg) of 10 students of a class are given below:
21, 28.5, 20.5, 24, 25.5, 22, 27.5, 28, 21 and 24.
Find the median of their weights.



Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk.
Milk (litre)1 - 33 - 55 - 77 - 99 - 1111 - 13
No. of hotels7515203518



The following table shows the classification of number of vehicles and their speeds on Mumbai-Pune express way. Find the median of the data.
Average Speed of vehicles
(km/hr)
60 - 6464 - 6970 - 7475 - 7979 - 8484 - 89
No. of vehicles10345585106



Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of mik.
Age (years):ess than 55 - 910 - 1415 - 1920 - 2425 - 29
No. of patients383250362420



Electricity used by some families is shown in the following table. Find the mode for use of electricity.
Use of electricity (Unit)0 - 2020 - 4040 - 6060 - 8080 - 100100 - 120
No of families1350701008017



In a basket, there are 10 tomatoes. The weight of each of these tomatoes in grams is as follows:
60, 70, 90, 95, 50, 65, 70, 80, 85, 95.
Find the median of the weights of tomatoes.



The following table shows the information regarding the milk collected from farmers on a milk collection centre and the content of fat in the milk, measured by a lactometer. find the mode of fat content.
Content of Fat (%)2 - 33  - 44 - 55 - 66 - 7
Milk collected (liter)3070806020



The distance covered by 250 public transport buses in a day is shown in the following frequency distribution table. Find the median of the distance.
Distance (km)200-210210-220220-230230-240240-250
No. of buses4060805020



The heights (in cm) of the volley-ball players from team A and team B were recorded as:
Team A: 180, 178, 176, 181, 190, 175, 187
Team B: 174, 175, 190, 179, 178, 185, 177
Find the median of team A and team B.



The production of electric bulbs in different factories is shown in the following table. Find the median of the productions.
No. of bulbs produced
(Thousands)
30 - 4040 - 5050 - 6060 - 7070 - 8080 - 9090 - 100
No. of factories12352015878



A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:
No. of Cars0 - 1010 - 2020 - 3030 - 4040 - 5050 - 6060 - 7070 - 80
Frequency71413122011158



The following table gives the distribution of lifetime of 400 neon lamps:
Find the median lifetime of the lamp.
1869663_79bcae285e5b467781c1fea6f7547c29.png



Write the formula to find median for grouped data.



The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
Runs scoredNumber of batsmen
3000 - 40004
4000 - 500018
5000 - 60009
6000 - 70007
7000 - 80006
8000 - 90003
9000 - 100001
10000 - 11,0001
Find the mode of the data.



Find the median of the data 15, 22 ,  9 , 20 , 6, 18 , 11 ,25 ,14.



A life insurance agent found the following data for the distribution of ages of 100 policyholders. Calculate the median age, if policies are given only to persons having age 18 years onwards bu less than 60 years
Age (in years)No. of policy holders
Below 202
Below 256
Below 3024
Below 3545
Below 4078
Below 4589
Below 5092
Below 5598
Below 60100
.



Find the median for the following frequency distribution table.
Class interval0 - 55 - 1010 - 1515 - 2020 - 2525 - 30
Frequency5391085



A life insurance agent found the following data for the distribution of ages of 100 policyholders. Calculate the median age, if policies are given only to persons having age 18 years onwards but lets than 60 years.
Age (in years)No. of policyholders (cf)
Below 202
Below 256
Below 3024
Below 3545
Below 4078
Below 4589
Below 5092
Below 5598
Below 60100



Find the median of the data 22 , 28 ,34  , 49 , 44  , 57 , 18 , 10 , 33  ,41 , 66 , 59 



The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table:
Find the median length of the leaves. (Hint: The data needs to be converted to continuous classes for finding the median since the formula assumes continuous classes. The classes then change to 117.5-126.5,126.5-135.5 171.5-180.5)
1869659_88a322ca8d294e0dafe9ee0d06a21df0.png



Find the coefficient of range of the following data - 
Size10 - 1515 - 2020 - 2525 - 30
Frequency2468



Find  the mean deviation from mean for the data 
4, 7, 8, 9, 10, 12, 13, 17



Find the mean deviation from mode for the data 
2, 2, 2.5, 2.1, 2.9, 2.8, 2.5, 2.3



Find the mean deviation from mode for the data 
2, 4, 6, 4, 8, 6, 4, 10, 4, 8



Find the mean deviation of circles in given table .
Diameter (mm)43-4647-5051-5455-5859-62
Number of circles1517212225



Find mean and variance for the data
x_{i}6101418242830
f_{i}24712843



Find the mode for the following data .
22 , 36 , 18 , 22 , 20 , 34 , 22  , 42, 46 , 42 



Find the mode for the following data .
4 , 3 , 1 , 5 , 3 , 7  , 9 , 6 



Find  the mean deviation from mean for the data 
28, 60, 38, 30, 32, 45, 53, 36, 44, 34



Find the mean deviation imaginary mean 35 for following distribution.
35, 25, 33, 50, 37, 33, 37, 30  



If value of all value terms of a series are same, then find value of dispersion 



Find median of the following variables values
25,34,33,13,20,26,36, 28,19,34



Find median from the following frequency distribution 
1877761_50c2c39edb5144318d54dac2d61d9904.png



Marks obtained by student of a class are given in the frequency distribution table. Find their median.
1877753_c7340e49f92c43798ff59cd763fd88ad.png



Find the mean and standard deviation of the following frequency distribution by step deviation method.
Class1-56-1011-1516-2021-2526-3031-35
Frequency 5718252041



Find median from the frequency distribution table
1877771_3cf0cbacc9534bc29d50309f61895f8d.png



Find the mean deviation about mode and its coefficient from the following data-
Central size6789101112
Frequency36913854



Marks obtained by 100 students are given in the table. Find their median.
1877751_a0e14aa9bd0741f1bd33dccae07bd885.png



Find the formula to find standard deviation in individual series 



Find the median of the data
19, 25, 59, 48, 35, 31, 30, 32, 51.
If 25 is replaces by 52 then find new median.



Find the dispersion of the following data centred size -
Central size32--3838-4444-5050-5656-6262-68
No. of student3691385



Number of children in 100 families are shown in the table. 
Find their median.
1877810_600f9c4045df4b258c71ac66cfdf9aa5.png



Find mode of the following distribution:
Class0 - 1010 - 2020 - 3030 - 4040 - 50
Frequency471393



Write importance of median.



  
1878119_1e1b93e4c6d74f7292cdbc116435fcb4.png



Find mode of the following distribution:
Class0 - 2020 - 4040 - 60 60 - 80 80 - 100
Frequency3152485



x0.10.20.30.40.50.60.7
f30602040105035



Find the median of the frequency distribution:
1877813_c57feb74e683402c810b465eb5cec2d1.png



Write the formula to find median by grouped frequency distribution.



Marks obtained by students in a class are given in the table. Find median
1877793_7bed49de122e4bacbeb5319eea64dd90.png



Find mode of the following frequency distribution
ClassFrequency
10 - 153
15 - 207
20 - 2516
25 - 3012
30 - 359
35 - 405
40 - 453



Find mode of the following data :
Class-interval0-2020-4040-6060-8080-100100-120120-140
Frequency681012653



Following data represents life period observations of electrical instruments.
Life period (in hrs)0-2020-4040-6060-8080-100100-120
Frequency1003552613829
Find mode of life period of instruments.



Following distribution represents weight of 30 students in a class. Find median weight of students.
Weight (in kg)40-4545-5050-5555-6060-6565-7070-75
No. of students2386632



If median of 17, 26, 60, 45, 33 is 33 and if 17 is replaced by 27 then what will be new median?



Find mode of the following frequency distribution
Height (in cm)52 - 5555 - 5858 - 6161 - 64
No. of students10 202510



Find mode of the following frequency distribution
Marks20 - 3030 - 4040 - 5050 - 6060 - 70
No. of students42842206



Find mode of the following data :
Class-intervalFrequency
80-8533
85-9027
90-9585
95-100155
100-105110
105-11045
110-11515



From the following data calculate standard deviation and its variability-
Marks10-2020-3030-4040-5050-6060-7070-8080-90
Students19324924521



Calculate standard deviation of the following:
X102030405060



Find the standard deviation for the following distribution:

Class

Frequency (f)

0-10

5

10-20

8

20-30

15

30-40

16

40-50

6



In a class of 40 students, marks obtained by the students in a class test (out of 10) are given below.
Marks12345678910
Number of students12336105433
Calculate the following for the given distribution:
Median



The Patel family flies from their home town, H, to Kiruna , K , in Lapland.
The Patel family has six suitcases. 
The number of items in each suitcase is shown below.
15        16       16       18       19       21
Write down the mode.
1912902_604ac94f40d144ff974dc61c6d16d9b2.png



The Patel family flies from their home town, H, to Kiruna , K , in Lapland.
The Patel family has six suitcases. 
The number of items in each suitcase is shown below.
15        16       16       18       19       21
Work out the median.
1912904_a1fc7ca885514175b6851623be1cb244.png



The numbers 42, 43, 44, 44, (2x + 3), 45, 45, 46, 47 have been put in the ascending order. If the median is 45, find x. Hence, find the mode of the above data.



In a class of 40 students, marks obtained by the students in a class test (out of 10) are given below.
Marks12345678910
Number of students12336105433
Calculate the following for the given distribution:
Mode



Find SD and Coefficient of variation.
Roll No. 12345678910
Marks50456040406065505670



Calculate the coefficient of variation:

Class

Frequency

0-10

5

10-20

8

20-30

10

30-40

15

40-50

12



Which measure of dispersion is the best and how?



Find the coefficient of variation from the following data:

Class

Frequency

10-20

4

20-30

5

30-40

6

40-50

2

50-60

3



Calculate the standard deviation from the following data:

Class

Frequency (f)

10-20

4

20-30

5

30-40

6

40-50

2

50-60

3



Define standard deviation and and formula.



In a certain examination, there were 100 candidates of whom 21 failed, 6 secured distinction, 12 were placed in the first division, 43 were placed in the third division and 18 in the second division. It is known that at least 75% marks are required for distinction, 40% for passing, 50% for second division and 60% for first division calculate median.



Calculate the standard deviation:

Class

Frequency

0-10

5

10-20

8

20-30

10

30-40

15

40-50

12



Following are the marks obtained by 10 students of a class. Calculate standard deviation and coefficient of standard deviation.
Marks 12, 8, 17, 13, 15, 9, 18, 11, 6, 1.



Fill in the blank:
_________________ is the value of variance when the standard deviation of a given series is 2.5.



Calculate the coefficient of variation using assumed mean method from the following information:

Weeks

COVID Patients (‘000)

0-4

600

4-8

400

8-12

250

12-16

200

16-20

300

20-24

350

24-28

450

28-32

500

32-36

750

36-40

900



Calculate coefficient of variation from the following data:

Marks

No. Of students

0-20

8

20-40

12

40-60

30

60-80

20

80-100

10



The number of books bought at a book fair by 200 students from a school are given in the following table:
No. of Books01234
No. of Students3564681815
Calculate the standard deviation.



Calculate the standard deviation of the following data :
x38131823
f71015108



Calculate the standard deviation of the following data
x38131723
f71015108



Let a, b, c, d and e be the observations with mean { m } and standard deviation S. The standard deviation of the observations a +  { k } ,b+ { k } ,c+ { k } , d+ { k } and e+ { k } is



Standard deviation of two distribution are same and their arithmetic means are 30 and 25 respectively. If their coefficient of variation is { v }_{ 1 } and{ v }_{ 2 }, then 6{ v }_{ 1 }-{ 5v }_{ 2 } is equal to ___________________.



Find the standard deviation of 10 observations 111, 211, 311,...... 1011.



The following table gives the daily wages of workers in a factory. Compute the standard deviation and the coefficient of variation of the wages of the workers.
Wages (Rs)125-175175-225225-275275-325325-375375-425425-475475-525525-575
Number of workers222191434611



Find the variance and standard devaiation of the following frequency distribution.
{ x }_{ i }6101418242830
{ f }_{ i }24712843
 



Find the standard deviation of the numbers 62,58,53,50,63,52,55.



A random variable x has the following probability distribution.
x=x-2-10123
P(x)0.1k0.22k0.3k
Find the value of k & calculate mean and variance of x.



The mean of 9 variates is 11. If eight of them are 7, 12, 9, 14, 21, 3, 8 and 15, find the 9th variate.



Using short ad method.find the man, variance and standard deviation for the data: 
Class0-1010-2020-2030-4040-50
Frequency5815166



Calculate standard deviation from the following data:

Marks (Less than)

Number of students (f)

20

8

40

20

60

50

80

70

100

80



Calculate coefficient of variation using step deviation method from the following information:

Class Interval

Frequency

0-5

15

5-10

10

10-15

11

15-20

12

20-25

6

25-30

6

30-35

10

35-40

15

40-45

10

45-50

5



Using short ad method.find the mean, variance and standard deviation for the data: 
Class25-3535-4545-5555-6565-75
Frequency6413215314051



Find the variance of the following data 6, 8, 10, 12, 14, 16 , 18, 20, 22, 24.



The frequency distribution table shows the number of mango trees in a groove and their yield of mangoes. Find the median of data.
No. of Mangoes50 - 100100 - 150150 - 200200 - 250250 - 300
No. of trees3330908017



Find out standard deviation of the following data:
Size12345678
Frequency510152025303540



Find out standard deviation of the following data:
Size10 12 14 16 
Frequency 5



Class 11 Engineering Maths Extra Questions