Loading [MathJax]/jax/output/CommonHTML/jax.js
MCQExams
0:0:2
CBSE
JEE
NTSE
NEET
Practice
Homework
×
CBSE Questions for Class 11 Commerce Applied Mathematics Descriptive Statistics Quiz 7 - MCQExams.com
CBSE
Class 11 Commerce Applied Mathematics
Descriptive Statistics
Quiz 7
The line graph represent the net sales rate of Apple company from the year
2003
−
2013
. Find the increase in sales rate during
2005
−
2007
.
Report Question
0%
16
,
000
millions
0%
8
,
000
millions
0%
26
,
000
millions
0%
32
,
000
millions
Explanation
The difference between the two sales rate of the year
2005
−
2007
is:
32
,
000
−
16
,
000
=
16
,
000
So, the increase in sales rate from the year
2005
−
2007
=
16
,
000
millions
According to the graph above, in which year was the ratio of the number of students enrolled at School
B
to the number of students enrolled at School
A
the
greatest?
Report Question
0%
1990
0%
1991
0%
1992
0%
1993
0%
1994
Explanation
As per given graph:
In year
1990
number of students enrolled at school
B
is
1200
and school
A
is
800
Then ratio of
B
to
A
=
1200
800
=
3
2
In year
1991
number of students enrolled at school
B
is
800
and school
A
is
1600
Then ratio of
B
to
A
=
800
1600
=
1
2
In year
1992
number of students enrolled at school
B
is
2000
and school
A
is
1200
Then ratio of
B
to
A
=
2000
1200
=
5
3
In year
1993
number of students enrolled at school
B
is
1600
and school
A
is
1600
Then ratio of
B
to
A
=
1600
1600
=
1
1
In year
1994
number of students enrolled at school
B
is
1600
and school
A
is
800
Then ratio of
B
to
A
=
1600
800
=
2
1
Then in year
1994
the ratio is greatest
So, answer is
(
E
)
,
1994
is correct.
The mean of a finite set X of numbers is
14
, the median of this set of numbers is
12
, and the standard deviation is
1.8
. A new set Y is formed by multiplying each member of the set S by
3
. Determine the correct statements w.r.t. set Y:
I. The mean of the numbers is set Y is
42
II. The median of the numbers in set Y is
36
III. The standard deviation of the numbers is set Y is
5.4
Report Question
0%
I only
0%
II only
0%
I and II only
0%
I and III only
0%
I, II, and III
Explanation
For set
x
Mean
=
14
Median
=
12
S.D.
=
√
σ
=
1.8
.
For set
y
Mean
=
14
×
3
=
42
.
Median
=
12
×
3
=
36
.
SD
=
1.8
×
3
=
5.4
.
Hence all three are correct.
How many watches were sold in all 5 months?
Report Question
0%
160
0%
180
0%
175
0%
170
Explanation
Total Sales= Addition of sales individually in each month.
Total Sale
=
20
+
50
+
20
+
60
+
30
=
180
Which year did the same number of boys and girls attend the conference?
Report Question
0%
1995
0%
1996
0%
1997
0%
1998
0%
None
Grades for the test on proofs did not go as well as the teacher had hoped. The mean grade was 68, the median grade was 64, and the standard deviation wasThe teacher curves the score by raising each score by a total of 7 points. Which of the following statements is true?
I. The new mean is 75.
II. The new median is 71.
III. The new standard deviation is 7.
Report Question
0%
I only
0%
III only
0%
I and II only
0%
I, II, and III
0%
None of the statements are true
Explanation
If each observation is increased by
7
then the mean will also be increased by
7
.
New Mean = Old Mean
+
7
=
68
+
7
=
75
If each observation is increased by
7
then the median will also be increased by
7
.
New median = Old median
+
7
=
64
+
7
=
71
If each observation is increased/decreased by any quantity the standard deviation will remain same.
New standard deviation= old standard deviation
=
12
The figure above shows the cost of joining and buying music from a music subscription service. What does the y-intercept of the line most likely represent?
Report Question
0%
The cost per song
0%
The cost to join the service
0%
The cost of buying 20 songs
0%
The cost of 20 subscriptions to the service
Explanation
When no. of songs are 0 then cost is 20
.
T
h
i
s
m
e
a
n
s
t
h
e
c
o
s
t
o
f
j
o
i
n
i
n
g
t
h
e
s
e
r
v
i
c
e
i
s
20
.
Hence, the y-intercept (i.e. 20) of the line represent the cost to join the service.
So, the answer is option (B).
In a final buzzer round of a competition, contestants were
asked to name as many states that begin with the letter
K
, by pressing the buzzer as early as possible., The bar graph shows the number of states the contestants were able to name. Find the number of contestants who participated in final buzzer round.
Report Question
0%
6
0%
8
0%
14
0%
20
Explanation
Arranging the data in tabular form gives us
No of states
→
1
2
3
4
5
6
7
8
Total
No of candidates who correctly answered them
→
1
1
5
6
4
0
2
1
20
Hence, the total number of participants were
20
.
A random variable
X
has the probability distribution given below. Its variance is
X
1
2
3
4
5
P(X=x)
k
2k
3k
2k
k
Report Question
0%
16
3
0%
4
3
0%
5
3
0%
10
3
Explanation
We know that
∑
P
(
x
)
=
1
k
+
2
k
+
3
k
+
2
k
+
k
=
1
9
k
=
1
k
=
1
9
Now, var
σ
2
=
∑
x
i
2
P
(
x
i
)
−
(
∑
x
i
P
(
x
i
)
)
2
=
1
(
k
)
+
2
2
(
2
k
)
+
3
2
(
3
k
)
+
4
2
(
2
k
)
+
5
2
(
k
)
−
[
1
(
k
)
+
2
(
2
k
)
+
3
(
3
k
)
+
4
(
2
k
)
+
5
(
k
)
]
2
=
93
k
−
(
27
k
)
2
=
93
(
1
9
)
−
[
27
(
1
9
)
]
2
=
31
3
−
3
2
=
31
−
27
3
=
4
3
What are the advantages of squaring a difference for calculating variance and standard deviation?
Report Question
0%
Squaring makes each term positive so that values above the mean do not cancel below the mean.
0%
Squaring adds more weight to the larger differences, and in many cases this extra weight is appropriate since points further from the mean may be more significant.
0%
It complicates the calculations
0%
All are incorrect
Explanation
Since,
σ
x
=
√
∑
(
x
i
−
ˉ
x
)
2
N
So, we can say that opion
A
and
B
are correct.
In how many of the given years was the production of fertilizers more than the average production of the given years?
Report Question
0%
1
0%
2
0%
3
0%
4
Explanation
Average production (in 10000 tonnes) over the given years
=
1
8
(
25
+
40
+
60
+
45
+
65
+
50
+
75
+
80
)
=
55
.
∴
The productions during the years 1997, 1999, 2001 and 2002 are more than the average production.
F
or how many companies has there been no decrease in production in any year from the previous year?
Report Question
0%
One
0%
Two
0%
Three
0%
Four
Explanation
By visual inspection, we can say that Honda, GM, and Maruti have not shown a decrease.
'
In which pair of years was the number of candidates qualified, the same?
Report Question
0%
1995 and 1997
0%
1995 and 2000
0%
1998 and 1999
0%
Data inadequate
Explanation
The graph gives the data for the percentage of candidates qualified to appeared and unless the absolute values of number of candidates qualified or candidates appeared is know we cannot compare the absolute values for any two years.
Hence, the data is inadequate to solve this question.
T
he difference in the sales of cellular phones for the years
1997
and
1999
is?
Report Question
0%
500
units
0%
1
,
000
units
0%
5
,
000
units
0%
18
,
000
units
Explanation
The given graph shows the sale of cellular phones in the years
1997
,
1998
,
1999
,
2000
,
2001
and
2002
.
In the year
1997
,
the sale of cellular phones is
48000
.
In the year
1999
,
the sale of cellular phones is
30000
.
Therefore, the difference in the sales of cellular phones for the year
1997
and
1999
is,
48000
−
30000
=
18000
Hence,
the difference in the sales of cellular phones for the year
1997
and
1999
is
18
,
000
units.
Thus, option
D
is correct.
Suppose a researcher is concerned with a nominal scale that identifies users versus nonusers of bank credit cards. The measure of central tendency appropriate to this scale is the
Report Question
0%
Mean
0%
Mode
0%
Median
0%
Average
Explanation
The mode is the value that appears most often in a set data. The mode of a discrete probability distribution is the value x at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled. The mode of a continuous probability distribution is the value x at which its probability density function has its maximum value, so the mode is at the peak.
Option B is correct.
T
he average production for five years was maximum for which company?
Report Question
0%
X
0%
Y
0%
Z
0%
X and Z both
Explanation
A
verage production (in lakh tons) in five years for the three companies are:
For Company X
=
[
1
5
×
(
30
+
45
+
25
+
50
+
40
)
]
=
190
5
=
38
For Company Y
=
[
1
5
×
(
25
+
35
+
35
+
40
+
50
)
]
=
185
5
=
37
For Company Z
=
[
1
5
×
(
35
+
40
+
45
+
35
+
35
)
]
=
190
5
=
38
∴
A
verage production of five years is maximum for both the Companies X and Z.
What was the percentage increase in imports from 1997 to 1998 ?
Report Question
0%
72
0%
56
0%
28
0%
Data inadequate
Explanation
The graph gives only the ratio of imports to exports for different years. To find the percentage increase in imports from 1997 to 1998, we require more details such as the value of imports or exports during these years.
Hence, the data is inadequate to answer this question.
The degree to which numerical data tend to spread about value is called
Report Question
0%
mean
0%
variation
0%
median
0%
mode
Explanation
Variance gives the degree to which the numerical data tend to spread about the value.
Variance is given by
∑
x
2
n
−
(
∑
x
n
)
2
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of
10
to each of the students. Which of the following statistical measures will not change even after the grace marks were given.
Report Question
0%
Median
0%
Mode
0%
Variance
0%
Mean
Explanation
The variance and standard deviation doesn't change even after addition of some constant to the given observations.
If
x
is increased by
k
then
σ
changes to
Report Question
0%
k
+
σ
0%
k
σ
0%
k
√
σ
0%
remains unchanged
Explanation
By the properties of standard deviation,
σ
(
x
+
k
)
=
σ
(
x
)
Therefore, by the addition of the constant, the standard deviation remains unchanged.
Variance of the first
11
natural numbers is:
Report Question
0%
√
5
0%
√
10
0%
5
√
2
0%
10
Explanation
Sum of first
n
natural numbers is
n
2
−
1
12
=
11
2
−
1
12
=
120
12
=
10
Thus, variance is
√
n
2
−
1
12
=
√
10
.
If
x
is multiplied by
k
then
σ
changes to
Report Question
0%
k
2
σ
0%
k
σ
0%
k
√
σ
0%
k
(
σ
)
2
Explanation
By the properties of standard deviation,
σ
(
k
x
)
=
|
k
|
σ
(
x
)
Therefore, by multiplying the
x
by
k
, SD changes to
k
σ
Standard Deviation of n observations
a
1
,
a
2
,
a
3
.
.
.
.
.
a
n
is
σ
Then the standard deviation of the observations
λ
a
1
,
λ
a
2
,
.
.
.
,
λ
a
n
is
Report Question
0%
λ
σ
0%
−
λ
σ
0%
|
λ
|
σ
0%
λ
n
σ
Explanation
Let the mean of original data is
μ
Then mean of observation if all the terms are multiplied by the constant
λ
will be
λ
μ
If
σ
be the standard deviation of original observation , then
σ
=
√
1
n
n
∑
i
=
1
(
x
i
−
μ
)
2
Now let the standard deviation of new observation is
σ
′
, then
σ
′
=
√
1
n
n
∑
i
=
1
(
λ
x
i
−
λ
μ
)
2
=
√
1
n
n
∑
i
=
1
λ
2
(
x
i
−
μ
)
2
=
|
λ
|
√
1
n
n
∑
i
=
1
(
x
i
−
μ
)
2
=
|
λ
|
σ
Note that: standard deviation can never be negative
The formula to find variance is
Report Question
0%
∑
x
2
n
−
(
∑
x
n
)
0%
∑
x
2
n
−
(
∑
x
n
)
2
0%
∑
x
2
n
−
(
¯
x
)
2
0%
∑
x
n
−
(
∑
x
n
)
2
Explanation
Variance gives the degree to which the numerical data tend to spread about the value.
Variance is given by
∑
x
2
n
−
(
∑
x
n
)
2
But mean
ˉ
x
=
∑
x
n
Therefore, variance is
∑
x
2
n
−
(
ˉ
x
)
2
The standard deviation of
a
,
a
+
d
,
a
+
2
d
,
.
.
.
,
a
+
2
n
d
is
Report Question
0%
n
d
0%
n
2
d
0%
√
n
(
n
+
1
)
3
d
0%
√
n
(
n
+
3
)
3
d
Explanation
Series is
a
,
a
+
d
,
a
+
2
d
,
⋯
,
a
+
2
n
d
Total number of terms:
N
=
2
n
+
1
Sum of the series:
S
=
2
n
+
1
2
(
a
+
a
+
2
n
d
)
=
(
2
n
+
1
)
(
a
+
n
d
)
Mean of the data:
ˉ
x
=
S
N
=
(
2
n
+
1
)
(
a
+
n
d
)
(
2
n
+
1
)
=
a
+
n
d
Standard Deviation:
s
.
d
.
=
√
2
n
+
1
∑
i
=
1
(
x
i
−
ˉ
x
)
2
N
s
.
d
.
=
√
2
(
1
2
+
2
2
+
⋯
+
n
2
)
(
2
n
+
1
)
=
2
×
n
(
n
+
1
)
(
2
n
+
1
)
6
(
2
n
+
1
)
d
2
s
.
d
.
=
√
n
(
n
+
1
)
3
d
If the variance of a data is
12.25
, then the standard deviation is
Report Question
0%
3.5
0%
3
0%
2.5
0%
3.25
Explanation
S
.
D
=
√
v
a
r
i
a
n
c
e
⇒
S
.
D
=
√
12.25
⇒
S
.
D
=
3.5
Option A is correct.
Find the variance of the following distribution.
Class interval
20
−
24
25
−
29
30
−
34
35
−
39
40
−
44
45
−
49
Frequency
15
25
28
12
12
8
Report Question
0%
416
0%
46
0%
16
0%
None of these
Explanation
C
l
a
s
s
M
i
d
−
p
o
i
n
t
(
x
)
F
r
e
q
u
e
n
c
y
(
f
)
x
f
(
x
−
¯
x
)
(
x
−
¯
x
)
2
(
x
−
¯
x
)
2
f
20
−
24
22
15
330
−
10.25
105.0625
1575.9375
25
−
29
27
25
675
−
5.25
27.5625
689.0625
30
−
34
32
28
896
−
0.25
0.0625
1.75
35
−
39
37
12
444
4.75
22.5625
270.75
40
−
44
42
12
504
9.75
95.0625
1140.75
45
−
49
47
8
376
14.75
217.5625
1740.5
∑
f
=
100
∑
x
f
=
3225
∑
(
x
−
¯
x
)
2
f
=
5418.75
⇒
M
e
a
n
(
¯
x
)
=
∑
x
f
∑
f
=
3225
100
=
32.25
⇒
V
a
r
i
a
n
c
e
(
σ
2
)
=
∑
(
x
−
¯
x
)
2
f
∑
f
=
5418.75
100
=
54.18
The mean and the variance of
10
observations are given to be
4
and
2
respectively. If every observation is multiplied by
2
, the mean and the variance of the new series will be respectively.
Report Question
0%
8
and
20
0%
8
and
4
0%
8
and
8
0%
80
and
40
Explanation
Mean is summation of all observations divided by number of observation and hence, would be multiplied by
2
due to linearity. Hence, the new mean is
8
.
Variance is sum of squares of each observation subtracted by the mean. Hence, due to squared dependence, it will be quadrupled to get
8
.
Hence, both mean and variance are
8
.
Calculate the standard deviation of the following data.
x
3
8
13
18
23
f
7
10
15
10
8
Report Question
0%
6.32
.
0%
2.32
.
0%
3.32
.
0%
None of these
Explanation
x
f
x
f
(
x
−
¯
x
)
(
x
−
¯
x
)
2
(
x
−
¯
x
)
2
f
3
7
21
−
10.2
104.04
728.28
8
10
80
−
5.2
27.04
270.4
13
15
195
−
0.2
0.04
0.6
18
10
180
4.8
23.04
230.4
23
8
184
9.8
96.04
768.32
∑
f
=
50
∑
x
f
=
660
∑
(
x
−
¯
x
)
2
=
1998
⇒
¯
x
=
∑
x
f
∑
f
=
660
50
=
13.2
Now, calculate standard deviation :
S
=
√
(
x
−
¯
x
)
2
∑
f
=
√
1998
50
=
√
39.96
=
6.32
What is the combined standard deviation of all 250 items ?
Report Question
0%
7.45
0%
7.35
0%
7.98
0%
7.73
Explanation
Here
n
1
=
100
,
ˉ
x
1
=
50
,
s
1
=
5
,
n
2
=
150
,
ˉ
x
2
=
40
,
s
2
=
6
∴
σ
=
√
n
1
s
2
1
+
n
2
s
2
2
n
1
+
n
2
+
n
1
n
2
(
ˉ
x
1
−
ˉ
x
2
)
2
(
n
1
+
n
2
)
2
=
√
100
(
5
)
2
+
150
(
6
)
2
100
+
150
+
(
100
)
(
150
)
(
50
−
40
)
2
(
100
+
150
)
2
=
√
158
5
+
24
=
√
31.6
+
24
=
√
55.6
=
7.45
∴
σ
=
7.45
Let X denote the number of scores which exceed 4 in 1 toss of a symmetrical die. Consider the following statements :
The arithmetic mean of X is
The standard deviation of X is
Which of the above statements is/are correct ?
Report Question
0%
1 only
0%
2 only
0%
Both 1 and 2
0%
Neither 1 nor 2
Explanation
The only possible favorable outcomes are
5
and
6
. Hence, the arithmetic mean of
X
is 5.5.
The standard deviation of
X
=
1
2
(
(
6
−
5.5
)
2
+
(
5
−
55
)
2
)
=
0.25
The variance of numbers
x
1
,
x
2
,
x
3
,
.
.
.
.
.
x
n
is V. Consider the following statements :
If every
x
1
, is increased by 2, the variance of the new set of numbers is V.
If the numbers
x
1
is squared, the variance of the new set is
V
2
.
Which of the following statements is/are correct ?
Report Question
0%
1 only
0%
2 only
0%
Both 1 and 2
0%
Neither 1 nor 2
Explanation
In case 1, a deterministic value of 2 units is being added to every
x
i
and hence, the variance of the set remains unchanged as
V
. New variance would be
1
n
∑
(
x
i
+
2
−
(
∑
x
i
+
2
n
)
)
=
1
n
∑
(
x
i
−
∑
x
i
n
)
=
V
In case 2, each
x
i
is squared and hence, the mean becomes
1
n
∑
x
2
i
. Hence, the new variance is
1
n
∑
(
x
2
i
−
1
n
∑
x
2
i
)
2
and not
V
2
=
1
n
2
∑
(
x
i
−
1
n
∑
x
i
)
4
.
Calculate the standard deviation of the first
13
natural numbers.
Report Question
0%
3.74
.
0%
2.74
.
0%
3.48
.
0%
None of these
Explanation
⇒
1
s
t
13
natural numbers are
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
,
11
,
12
,
13.
∑
x
=
n
(
n
+
1
)
2
=
13
(
13
+
1
)
2
=
13
×
14
2
∴
∑
x
=
91
Now,
∑
x
2
=
n
(
n
+
1
)
(
2
n
+
1
)
6
=
13
×
14
×
27
6
∴
∑
x
2
=
819
⇒
S
D
=
√
∑
x
2
n
−
(
∑
x
n
)
2
=
√
819
13
−
(
91
13
)
2
=
√
63
−
49
=
√
14
=
3.74
The variance of first '
n
' natural number is
Report Question
0%
n
2
+
1
12
0%
n
2
−
1
12
0%
(
n
+
1
)
(
2
n
+
1
)
6
0%
None of these
Explanation
By using formula of variance, we have
σ
2
=
1
n
n
∑
i
=
1
x
2
i
−
(
1
n
n
∑
i
=
1
x
i
)
2
=
1
n
(
1
2
+
2
2
+
⋯
+
n
2
)
−
(
1
n
(
1
+
2
+
⋯
+
n
)
)
2
=
1
n
⋅
n
(
n
+
1
)
(
2
n
+
1
)
6
−
1
n
2
⋅
[
n
(
n
+
1
)
2
]
2
=
(
n
+
1
)
(
2
n
+
1
)
6
−
(
n
+
1
)
2
4
=
n
2
−
1
12
Calculate the standard deviation of the following data.
10
,
20
,
15
,
8
,
3
,
4
Report Question
0%
5.97
0%
59.7
0%
4.97
0%
None of these
Explanation
⇒
The given numbers are
3
,
4
,
8
,
10
,
15
,
20
.
⇒
¯
X
=
3
+
4
+
8
+
10
+
15
+
20
6
=
10
X
X
−
¯
X
(
X
−
¯
X
)
2
3
−
7
49
4
−
6
36
8
−
2
4
10
0
0
15
5
25
20
10
100
∑
(
X
−
¯
X
)
2
=
214
⇒
S
=
√
(
X
−
¯
X
)
2
N
=
√
214
6
=
√
35.66
=
5.97
What is the ratio of the total sales of branch B2 for both years to the total sales of branch B4 for both years?
Report Question
0%
2:3
0%
3:5
0%
4:5
0%
7:9
Explanation
Total sale of
B
2
=
75
+
65
=
140
Total sale of
B
4
=
85
+
95
=
180
Ratio of sales of
B
2
and
B
4
=
140
180
=
7
9
So option
D
is correct.
If the mean of the numbers
a
,
b
,
8
,
5
,
10
is
6
and their variance is
68
, then
a
b
is equal to
Report Question
0%
6
0%
7
0%
12
0%
14
0%
25
Explanation
Given,
a
+
b
+
8
+
5
+
10
5
=
6
⇒
a
+
b
+
c
+
23
=
30
⇒
a
+
b
=
7....
(
i
)
and
∑
(
x
1
−
¯
x
)
2
n
=
σ
2
(
a
−
6
)
2
+
(
b
−
6
)
2
+
4
+
1
+
16
5
=
34
5
⇒
(
a
−
6
)
2
+
(
b
−
6
)
2
+
21
=
34
⇒
a
2
+
b
2
−
84
+
93
=
34
[
∵
a
+
b
=
7
]
⇒
a
2
+
b
2
=
25...
(
i
)
From Eq.(i)
⇒
(
a
+
b
)
2
=
7
2
⇒
a
2
+
b
2
+
2
a
b
=
49
⇒
25
+
2
a
b
=
49
(From Eq.(ii))
⇒
2
a
b
=
24
⇒
a
b
=
12
For the data set below, which value is in the 75th percentile?
1
,
3
,
3
,
4
,
6
,
7
,
7
,
7
,
8
,
9
,
9
,
10
,
12
,
15
,
16
,
17
Report Question
0%
16
0%
9
0%
12
0%
15
Explanation
1
,
3
,
3
,
4
,
6
,
7
,
7
,
7
,
8
,
9
,
9
,
10
,
12
,
15
,
16
,
17
Logic:- first quartile lies halfway between the lowest valve of the Median & the third Quartile lies halfway between the Median & the largest value.
N
=
16
Third quartile or
75
percentile
=
3
(
n
+
1
)
4
th term
=
3
×
17
4
=
12.75
t
h
term
=
12
t
h
term
+
0.75
×
(
13
t
h
term
−
12
t
h
term
)
=
10
+
0.75
×
(
12
−
10
)
=
10
+
0.75
×
2
=
11.5
≈
12
.
What is the total expenditure (Rs. in lakhs) of the company during the period January to July in the year 2003?
Report Question
0%
3
,
800
0%
3
,
950
0%
4
,
600
0%
5
,
350
Explanation
Required expenditure of the company
=
600
+
500
+
500
+
650
+
500
+
600
+
600
3950
lakh
If the variance of
1
,
2
,
3
,
4
,
5
,
.
.
.
,
x
is
10
, then the value of
x
is
Report Question
0%
9
0%
13
0%
12
0%
10
0%
11
Explanation
We know that, the variance of first
x
natural number is
Var
(
x
)
=
x
2
−
1
12
=
10
....(given)
⇒
x
2
=
120
+
1
=
121
⇒
x
=
11
For the information given below,Find quartile deviation and coefficient of quartile deviation
Maximum Load
Number of Cables
9.3-9.7
22
9.8-10.2
55
10.3-10.7
12
10.8-11.2
17
11.3-11.7
14
11.8-12.2
66
12.3-12.7
33
12.8-13.2
11
Report Question
0%
0.275
,
0.065
0%
0.495
,
0.045
0%
0.415
,
0.055
0%
0.225
,
0.012
Explanation
M
a
x
i
m
u
m
l
o
a
d
N
o
.
o
f
c
a
b
l
e
s
C
l
a
s
s
b
o
u
n
d
a
r
i
e
s
C
u
m
u
l
a
t
i
v
e
f
r
e
q
u
e
n
c
y
9.3
−
9.7
2
9.25
−
9.75
2
9.8
−
10.2
5
9.75
−
10.25
7
10.3
−
10.7
12
10.25
−
10.75
19
10.8
−
11.2
17
10.75
−
11.25
36
11.3
−
11.7
14
11.25
−
11.75
50
11.8
−
12.2
6
11.75
−
12.25
56
12.3
−
12.7
3
12.25
−
12.75
59
12.8
−
13.2
1
13.25
60
Q
1
:
Value of
n
4
t
h
=
60
4
=
15
t
h
∴
Q
1
lies in class
10.25
−
10.75
Where,
l
=
10.25
,
h
=
0.5
,
f
=
12
,
c
f
=
7
Q
1
=
l
+
h
f
(
n
4
−
c
.
f
.
)
=
10.25
+
0.5
12
(
15
−
7
)
=
10.25
+
0.33
=
10.58
Q
3
:
Value of
3
n
4
t
h
i
t
e
m
=
3
×
60
4
=
45
t
h
i
t
e
m
∴
Q
3
lies in class
11.25
−
11.75
Here,
l
=
11.25
,
h
=
0.5
,
f
=
14
,
3
n
4
=
45
and
c
f
=
36
Q
3
=
l
+
h
f
(
3
n
4
−
c
.
f
)
=
11.25
+
0.5
14
(
45
−
36
)
=
11.25
+
0.32
=
11.57
⇒
Now, Quartile deviation
=
Q
3
−
Q
1
2
=
11.57
−
10.58
2
=
0.99
2
=
0.495
⇒
Coefficient of Quartile Deviation
=
Q
3
−
Q
1
Q
3
+
Q
1
=
11.57
−
10.58
11.57
+
10.58
=
0.99
22.15
=
0.045
The arithmetic mean of the observations 10,8,5,a,b is 6 and their variance 6.Then ab=
Report Question
0%
6
0%
4
0%
3
0%
12
Explanation
10
+
8
+
5
+
a
+
b
5
=
6
,
1
n
∑
(
x
i
−
¯
x
)
2
=
6.8
solving above two equations we get values of a and b.
Mean of
10
observations is
50
and their standard deviation is
10
. If each observation is subtracted by
5
and then divided by
4
, then the new mean and standard deviation are
Report Question
0%
22.45
,
2.5
0%
11.25
,
2.5
0%
11.5
,
2.5
0%
11
,
2.5
0%
11.75
,
2.5
Explanation
Given,mean of
10
observations
=
10
∑
i
=
1
x
i
10
=
50
⇒
10
∑
i
=
1
x
i
=
500
.... (i)
Therefore, new mean
=
10
∑
i
=
1
x
i
−
5
×
10
4
×
10
=
500
−
50
4
×
10
[using Eq. (i)]
=
450
4
×
10
=
11.25
and standard deviation
=
old
(
S
D
)
4
=
10
4
=
2.5
.
What is the average monthly expenditure (Rs. in lakhs) for January to July during the year 2005?
Report Question
0%
658.3
0%
766.7
0%
764.2
0%
657.1
Explanation
Required average
=
700
+
750
+
850
+
850
+
600
+
750
+
850
7
=
5350
7
=
764.2
lakh
The line graph show the number of cars Jatin sold over the past
5
weeks.
If he was paid
R
s
20000
for every car sold, how much was he paid over the past
5
weeks?
Report Question
0%
R
s
280000
0%
R
s
240000
0%
R
s
480000
0%
R
s
500000
Explanation
Total number of cars sold by jatin in week
1
=
2
Total number of cars sold by jatin in week
2
=
4
Total number of cars sold by jatin in week
3
=
3
Total number of cars sold by jatin in week
4
=
6
Total number of cars sold by jatin in week
5
=
9
Therefore Total numbers of cars sold upto
5
weeks =
2
+
4
+
3
+
6
+
9
=
24
For every caar sold , he paid
20000
Rs
So for 24 cars he would have paid=
20000
×
24
=
480000
.
The given pictograph shows the number of wall clocks sold by a company during a week. Each clock in the pictograph represents
5
wall clocks. How many wall clocks were sold during the week?
Report Question
0%
101
0%
110
0%
120
0%
115
Explanation
Total number of wall clocks sold =
20
+
25
+
15
+
35
+
10
+
5
=
110
Hence the correct answer is option B.
Which of the above states is the largest producer of wheat?
Report Question
0%
M.P.
0%
Haryana
0%
Maharashtra
0%
U.P.
Explanation
From the given graph, U.P. has highest production of wheat with
16
million tonnes being produced, and has tallest bar.
If the sum and sum of squares of
10
observations are
12
and
18
resp., then, The
S
.
D
of observations is :-
Report Question
0%
1
5
0%
2
5
0%
3
5
0%
4
5
Explanation
∑
x
=
12
,
∑
x
2
=
18
,
N
=
10
S
D
=
√
∑
x
2
N
−
(
∑
x
N
)
2
⟹
S
D
=
√
18
10
−
(
12
10
)
2
=
3
5
An Um contains
4
white and
3
red balls.
X
is the no. of red balls. Find the Mean and Variance of
X
.
Report Question
0%
9
7
,
24
49
0%
9
7
,
25
48
0%
9
8
,
24
49
0%
9
8
,
24
48
Explanation
Let x be the no. of red balls in a random draw of three balls. As these are
8
red balls, double value of x are
0
,
1
,
2
,
3
p
(
0
)
=
3
C
o
×
4
C
3
7
C
3
=
4
×
3
×
2
7
×
6
×
5
=
4
35
p
(
1
)
=
3
C
1
×
4
C
2
7
C
3
=
3
×
6
×
6
7
×
6
×
5
=
18
35
p
(
2
)
=
3
C
2
×
4
C
1
7
C
3
=
3
×
4
×
6
7
×
6
×
5
=
12
35
p
(
3
)
=
3
C
3
×
4
C
3
7
C
3
=
1
×
1
×
6
7
×
6
×
5
=
1
35
for calculation of mean of variance
x p(x) xp(x)
x
2
p
(
x
)
0
4
/
35
0
0
1
18
/
35
18
/
35
18
/
35
2
12
/
35
24
/
35
40
/
35
3
1
/
35
3
/
35
9
/
35
Total
1
9
/
7
15
/
7
Mean
=
∑
x
p
(
x
)
=
9
7
variance
=
∑
x
2
⋅
p
(
x
)
−
(
∑
x
.
p
(
x
)
)
2
=
15
7
−
81
49
=
24
49
.
Find the Quartile Deviation for the following set of data:
490
,
540
,
590
,
600
,
620
,
650
,
680
,
770
,
830
,
840
,
890
,
900
Report Question
0%
12
0%
122.5
0%
13
0%
12.6
Explanation
490
,
540
,
590
,
600
,
620
,
650
,
680
,
770
,
830
,
840
,
890
,
900
Q
d
=
Q
3
−
Q
1
2
Q
d
→
Quality deviation
Q
1
→
25
t
h
perentile
Q
3
→
75
t
h
perentile
Q
1
=
(
n
+
1
4
)
th term
=
13
4
th term
=
3.25
th term
=
3
r
d
term
+
0.25
×
(
4
t
h
term
−
3
r
d
term
)
=
590
+
0.25
×
(
600
−
590
)
=
590
+
0.25
×
10
Q
1
=
592.5
Q
3
=
3
(
n
+
1
)
4
th term
=
3
4
×
13
=
9.75
t
h
term
=
9
t
h
term
+
0.75
×
(
10
t
h
term
−
9
t
h
term
)
=
830
+
0.75
×
(
840
−
830
)
=
830
+
7.5
Q
3
=
837.5
Q
d
=
Q
3
−
Q
1
2
=
837.5
−
592.5
2
=
245
2
=
122.5
.
0:0:2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0
Answered
1
Not Answered
49
Not Visited
Correct : 0
Incorrect : 0
Report Question
×
What's an issue?
Question is wrong
Answer is wrong
Other Reason
Want to elaborate a bit more? (optional)
Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers
<
>
Support mcqexams.com by disabling your adblocker.
×
Please disable the adBlock and continue.
Thank you.
Reload page