MCQ Questions for Class 11 Commerce Economics Measures Of Central Tendency Quiz 14

Which of the following statements is true?

0%
Usually mean is the best measure of central tendency
0%
Usually median is the best measure of central tendency
0%
Usually mode is the best measure of central tendency
0%
Normally, GM is the best measure of central tendency

Extreme values have _______ effect on mode.

0%
a large
0%
a small
0%
no
0%
None of above

The following table gives the marks obtained by

$300$ students of a management course. Find the median of the distribution.

Marks obtained	No. of students
$0 - 15$	$26$
$15 - 30$	$34$
$30 - 45$	$64$
$45 - 60$	$76$
$60 - 75$	$60$
$75 - 90$	$60$
$90 - 100$	$10$

0%
$62.96$ marks
0%
$62.13$ marks
0%
$50.13$ marks
0%
$50.96$ marks

$10, 19, 22, 16, 15, 18, 20, 18, 14, 18, 23$
The median of the observations above is _________.

0%
$17.55$
0%
$18$
0%
$15$
0%
$16.5$

Consider following frequency distribution.

Class Intervals	$0-10$	$10-20$	$20-30$	$30-40$
Frequency	$8$	$10$	$12$	$15$

Arithmetic mean

$=$ ?

0%
$39.65$
0%
$22.55$
0%
$32.55$
0%
$23.56$

The average rainfall for a week, excluding Sunday, was

$10\ \text{cms}$ . Due to heavy rainfall on Sunday, the average for the week rose to

$15\ \text{cms}$ . How much rainfall was on Sunday?

0%
$25\ \text{cms}$
0%
$35\ \text{cms}$
0%
$45\ \text{cms}$
0%
$55\ \text{cms}$

What is the value of median for the following data:

Marks	No. of Students
$5 - 14$	$10$
$15 - 24$	$18$
$25 - 34$	$32$
$35 - 44$	$26$
$45 - 54$	$14$
$55 - 64$	$10$

0%
$28$
0%
$30$
0%
$32.94$
0%
$33.18$

The average marks of three batches of students having 70, 50 and 30 students respectively are 50, 55 andFind the average marks of all the 150 students, taken together.

0%
$50.67$
0%
$40.67$
0%
$50.60$
0%
$40.60$

Explanation

Given that, the average marks of 70, 50 and 30 students respectively are 50, 55 and 45 marks.

$\therefore\$ the total marks of 70, 50 and 30 students will be,

$70 \times 50, 50 \times 55$ and

$30 \times 45$ respectively.

The average marks of all the 150 students will be:

$= \dfrac{ (3500 + 2750 + 1350 )}{( 70+50+30)}$

$\left[\text{Average}=\dfrac{\text{Sum of all quantities}}{\text{Number of quantities}}\right]$

$\Rightarrow \dfrac{7,600 }{150}$

$\Rightarrow 50.67$

Hence, the average marks of all the 150 students, taken together are

$50.67$

What percentage of value lies between

$5th$ and

$25th$ percentiles?

0%
$20\%$
0%
$30\%$
0%
$75\%$
0%
None of the above

Which of the deciles are less than first quartile?

0%
$D_1 and D_3$
0%
$D_1 and D_4$
0%
$D_1 and D_2$
0%
None of the above

Consider the following observation relating to marks obtained by

$10$ students in CS Foundation Exam:

$201, 202, 207, 222, 276, 201, 246, 212, 285, 312$ .
Arithmetic mean

$=$ ?

0%
$206$
0%
$237.3$
0%
$217.2$
0%
$216.1$

Explanation

Mean refers to the average amount in a given group of data. In this measure of central tendency, all the data are added up and then divided by the number of figures in the data in order to ascertain the mean.

Mean

$\dfrac{(201+ 202+207+222+276+201+246+212+285+312}{10}$

$= 236.4$

Find median of the following data.

Age greater than (Years)	No. of Persons
$0$	$230$
$20$	$218$
$30$	$200$
$40$	$165$
$50$	$123$
$60$	$73$
$70$	$288$

0%
$31.5$
0%
$41.5$
0%
$41.6$
0%
$31.6$

Find the median of the given mentioned observation

$15, 20, 45, 30, 60, 36$ .

0%
$32$
0%
$33$
0%
$47.5$
0%
None of the above

The numerical value separating the higher half of a sample from a lower half is?

0%
Median
0%
Mode
0%
Mean
0%
Standard deviation

The average of five numbers is

$40$ and the average of another six numbers is

$50$ . The average of all numbers taken together is _______.

0%
$44.44$
0%
$45.00$
0%
$45.45$
0%
$90.00$

Explanation

The average of five numbers is 40 , so the total of these five numbers will be 5x40.

The average of another six numbers is 50 , so the total of these six numbers will be 6x50.

Therefore, the average of all these taken together will be

$= \dfrac{( 200+ 300)}{5+6}$

$= \dfrac{500}{11 }$

$= 45.45$

The variate values which divide a series (frequency distribution) into

$100$ equal parts are called ______.

0%
quintiles
0%
quartiles
0%
deciles
0%
percentiles

Which of the following statements about the median is NOT true?

0%
It is more affected by extreme values than the mean
0%
It is the middle value that separates the upper half from the lower half
0%
It is equal to the mode in bell-shaped distributions
0%
Both b & c

For calculation of median through interpolation formulae

$"h"$ in the formulae is?

0%
Frequency of the median
0%
Lower limit of the median class
0%
Width of the median class
0%
Median

A measure of central tendency that attempts to describe a set of data by identifying the central position within the data is?

0%
Mean
0%
Mode
0%
Median
0%
All the above

If the two observations are

$10$ and

$0$ , their arithmetic mean is _______.

0%
$10$
0%
$0$
0%
$5$
0%
none of the above

Explanation

Arithmetic mean refers to the average amount in a given group of data. In this measure of central tendency, all the data are added up and then divided by the number of figures in the data in order to ascertain the mean.

Therefore,

Arithmetic mean

$= \dfrac{(10+0)}{2}$

$= \dfrac{10}{2}$

$= 5$

The formulae for calculating the median if individual observations are given will be.

0%
$(N+1)/2$ th if n is add
0%
$(N+1)th/2$ if n is even
0%
$(N/2)$ th if n is even
0%
Both a & c

A measure of central location which splits the data set into two equal groups is called the.

0%
Mean
0%
Mode
0%
Median
0%
Standard deviation

The mean is_____________________.

0%
the statistical or arithmetic average
0%
the middlemost score
0%
the most frequently occurring score
0%
the best representation for every set of data

Explanation

Mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean like direct method where all the data are added up and then divided by the number of figures in the data in order to ascertain the mean class or assumed mean method and step deviation method, the data of the given class is reduced into smaller units which makes it easy to do calculation and ascertain the mean of the class.

i.e.

$Arithmetic\ mean= \dfrac{Sum\ of\ given\ numbers}{Total\ numbers}$

Given the following data set, what is the value of median (2 4 3 6 1 8 9 2 5 7 ).

0%
2
0%
4.7
0%
4.5
0%
10

Consider the following frequency distribution.

Class Intervals	$0-10$	$10-20$	$20-30$	$30-40$
Frequency	$8$	$10$	$12$	$15$

Arithmetic mean

$=$ ?

0%
$39.65$
0%
$22.55$
0%
$32.55$
0%
$23.56$

Explanation

Class Intervals	Mid-values(x)	Frequency(f)	fx
$01-0$	$5$	$8$	$40$
$10-20$	$15$	$10$	$150$
$20-30$	$25$	$12$	$300$
$30-40$	$35$	$15$	$525$
		$\displaystyle\sum f=45$	$\displaystyle\sum fx =1,015$

Arithmetic mean

$=\dfrac{1,015}{45}=22.55$ .

The average (arithmetic mean) of a set of seven numbers is

$8$ . When an eighth number is added to the set, the average of the eight numbers is still

$8$ . What number was added to the set?

0%
$6$
0%
$7$
0%
$8$
0%
$9$

Following is arranged in ascending order. If the median of the data is

$63$ , find the volume of x in a series

$29, 32, 48, 50, x, x+2, 72, 78, 84, 95$ .

0%
$60$
0%
$62$
0%
$63$
0%
$64$

The following is the distribution of weekly wages of workers in a factory. Calculate the arithmetic mean of the distribution.

Weekly Wages (Rs.)	No. of Workers
$240-269$	$7$
$270-299$	$19$
$300-329$	$27$
$330-359$	$15$
$360-389$	$12$
$390-419$	$12$
$420-449$	$8$

0%
$352.3$
0%
$344.5$
0%
$226.7$
0%
$336.7$

Explanation

Class Intervals	Mid-values (x)	Frequency(f)	fx
$240-269$	$254.5$	$7$	$1,781.5$
$270-299$	$284.5$	$19$	$5,405.5$
$300-329$	$314.5$	$27$	$8,491.5$
$330-359$	$344.5$	$15$	$5,167.5$
$360-389$	$374.5$	$12$	$4,494$
$390-419$	$404.5$	$12$	$4,854$
$420-449$	$434.5$	$8$	$3,476$
		$\displaystyle\sum f=100$	$\displaystyle\sum fx=33,670$

Arithmetic mean

$=33,670/100=336.7$ .

The arithmetic mean between

$\cfrac { x+a }{ x }$ and

$\cfrac { x-a }{ x }$ when

$x\ne 0$ , is (the symbol

$\ne$ means "not equal to"):

0%
$2$ , if $a\ne 0$
0%
$1$
0%
$1$ , only if $a=0$
0%
$\dfrac {a}{x}$
0%
$x$

Explanation

The arithmetic mean between two quantities is given by,

A.M.=

$\dfrac{\dfrac{x+a}{x}+\dfrac{x-a}{x}}{2}$

$\dfrac{x+a+x-a}{2x}$

$\dfrac{2x}{2x}$

Hence A.M.=1

Find the value of

$p$ , if the mean of the following distribution is

$20$ .

$x$ :	$15$	$17$	$19$	$20+p$	$23$
$f$ :	$2$	$3$	$4$	$5p$	$6$

0%
$1$
0%
$2$
0%
$3$
0%
$4$

Explanation

Mean =

$\dfrac {\sum x_{i} f_{i}} {\sum f_{i}}$

$\Rightarrow$ mean = $\dfrac {(15\times 2)+(17\times 3)+(19 \times 4)+((20+p) \times 5p)+(23 \times 6)}{2+3+4+5p+6}$

$\Rightarrow$ mean =

$\dfrac {30+51+76+(20+p)(5p)+138}{2+3+4+5p+6}=20$

$\Rightarrow 295+100p+5p^{2}=300+100p$

$\Rightarrow 5p^{2}=5$

$\Rightarrow p=1$

CBSE Questions for Class 11 Commerce Economics Measures Of Central Tendency Quiz 14 - MCQExams.com

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Practice Class 11 Commerce Economics Quiz Questions and Answers

Class Intervals	0−10	10−20	20−30	30−40
Frequency(f)	8	10	12	15
Class mark ( mid points= x)	5	15	25	35
Fx	40	150	300	525

Marks	No. of Students
4.5 −14.5	10
14.5 −24.5	18
24.5 −34.5	32
34.5 −44.5	26
44.5−54.5	14
54.5−64.5	10

CBSE Questions for Class 11 Commerce Economics Measures Of Central Tendency Quiz 14 - MCQExams.com

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Practice Class 11 Commerce Economics Quiz Questions and Answers

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