Statistics class 10 questions with solutions

Q 1 :

The sum of the lower limit of median class and the upper limit of the modal class of the following data is:

Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60

No. of students 8 10 12 22 30 18

70
80
90
100

1

2

3

4

(2) 80

Q 2 :

For the following distribution:

Class 0-5 5-10 10-15 15-20 20-25

Frequency 10 15 12 20 9

the sum of lower limits of the median class and modal class is

15
25
30
35

1

2

3

4

(2)

Class	Frequency (f)	c.f.
0 - 5	10	10
5 - 10	15	25
10 - 15	12	37
15 - 20	20	57
20 - 25	9	66
	N = 66

Since, $N = 66,$ then $\frac{N}{2} = 33$

and cumulative frequency greater than or equal to 33 lies in class 10 – 15
So, median class is 10 – 15

$∴$ Lower limit of median class is 10

and highest frequency is 20 lie in class 15 – 20
So, modal class is 15 – 20.

$∴$ Lower limit of modal class is 15.

Hence, sum of lower limits of the median and modal class is 10 + 15 = 25.

Q 3 :

If the difference of Mode and Median of a data is 24, then the difference of median and mean is

8
12
24
36

1

2

3

4

(2)

mode – median = 24 (given)

$∴$ mode = 24 + median

Since, mode = 3 median – 2 mean [By empirical relation]

$∴$ 24 + median = 3 median – 2 mean

⇒ 2 median – 2 mean = 24

⇒ median – mean = 12

Q 4 :

The middle most observation of every data arranged in order is called

mode
median
mean
deviation

1

2

3

4

(2)

The middle most observation, after arranging all observations in ascending or descending order is called the median.

Q 5 :

For some data $x_{1}, x_{2}, \dots, x_{n}$ with respective frequencies $f_{1}, f_{2}, \dots, f_{n}$ , the value of $\sum_{1}^{n} f_{i} (x_{i} - \bar{x})$ is equal to:

$n \bar{x}$
$1$
$\sum f_{i}$
$0$

1

2

3

4

(4) 0

Q 6 :

After an examination, a teacher wants to know the marks obtained by maximum number of the students in her class. She requires to calculate ................. of marks.

median
mode
mean
range

1

2

3

4

(2)

Mode = The Most Common or (Maximum). Number that appears in your set of data.

Q 7 :

If value of each observation in a data is increased by 2, then median of the new data

increases by 2
increases by 2n
remains same
decreases by 2

1

2

3

4

(1)

When value of each observation in data is increased by 2.

So, median of data is Increases by 2

Q 8 :

For some data $x_{1}, x_{2}, \dots, x_{n} w i t h r e s p e c t i v e f r e q u e n c i e s f_{1}, f_{2}, \dots, f_{n}, t h e v a l u e o f \sum_{i = 1}^{n} f_{i} (x_{i} - x)$ is equal to:

$n x$
1
$\sum f_{i}$
0

1

2

3

4

(4)

$\sum_{i = 1}^{n} f_{i} (x_{i} - x) = f 1 (x 1 - x) + f 2 (x 2 - x) + \dots + f n (x n - x) = (f_{1} x_{1} + f_{2} x_{2} + \dots + f_{n} x_{n}) - (f_{1} x + f 2 x + \dots + f n x) = \sum_{i = 1}^{n} f_{i} x_{i} - x i = 1 n f i = \sum_{i = 1}^{n} f_{i} x_{i} - \frac{\sum_{i = 1}^{n} f_{i} x_{i}}{\sum_{i = 1}^{n} f_{i}} \cdot \sum_{i = 1}^{n} f_{i} = 0 x = \frac{\sum_{i = 1}^{n} f_{i} x_{i}}{\sum_{i = 1}^{n} f_{i}}$

Q 9 :

If every term of the statistical data consisting of n terms is decreased by 2, then the mean of the data:

decreases by 2
remains unchanged
decreases by 2n
decreases by 1

1

2

3

4

(1)

Let n terms of data be

$x_{1}, x_{2}, x_{3}, \dots, x_{n} . ∴ Mean (\bar{x}) = \frac{\sum_{i = 1}^{n} x_{i}}{n} N o w, w h e n e a c h t e r m i s d e c r e a s e d b y 2 . ∴ D a t a w i l l b e x_{1} - 2, x_{2} - 2, x_{3} - 2, \dots, x_{n} - 2 ∴ N e w m e a n = = \frac{\sum_{i = 1}^{n} (x_{i} - 2)}{n} = \frac{\sum_{i = 1}^{n} x_{i}}{n} - \frac{2 n}{n} = \bar{x} - 2 \Rightarrow " M e a n i s a l s o d e c r e a s e d b y 2 . "$

Q 10 :

If the mean of the first n natural numbers is 15, then value of n is:

28
29
30
31

1

2

3

4

(2)

We have, mean of first n natural numbers

= $\frac{n (n + 1)}{2 n} \Rightarrow 15 = \frac{(n + 1)}{2} \Rightarrow n + 1 = 30 \Rightarrow n = 30 - 1 = 29 ∴ n = 29$

Topic Question Set

Q 1 :

The sum of the lower limit of median class and the upper limit of the modal class of the following data is:

Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60

No. of students 8 10 12 22 30 18

Q 2 :

For the following distribution:

Class 0-5 5-10 10-15 15-20 20-25

Frequency 10 15 12 20 9

the sum of lower limits of the median class and modal class is

Q 3 :

If the difference of Mode and Median of a data is 24, then the difference of median and mean is

Q 4 :

The middle most observation of every data arranged in order is called

Q 5 :

For some data $x_{1}, x_{2}, \dots, x_{n}$ with respective frequencies $f_{1}, f_{2}, \dots, f_{n}$ , the value of $\sum_{1}^{n} f_{i} (x_{i} - \bar{x})$ is equal to:

Q 6 :

After an examination, a teacher wants to know the marks obtained by maximum number of the students in her class. She requires to calculate ................. of marks.

Q 7 :

If value of each observation in a data is increased by 2, then median of the new data

Q 8 :

For some data $x_{1}, x_{2}, \dots, x_{n} w i t h r e s p e c t i v e f r e q u e n c i e s f_{1}, f_{2}, \dots, f_{n}, t h e v a l u e o f \sum_{i = 1}^{n} f_{i} (x_{i} - x)$ is equal to:

Q 9 :

If every term of the statistical data consisting of n terms is decreased by 2, then the mean of the data:

Q 10 :

If the mean of the first n natural numbers is 15, then value of n is:

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Marks	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
No. of students	8	10	12	22	30	18

Topic Question Set

Q 4 : The middle most observation of every data arranged in order is called .question-row { display: flex; align-items: flex-start; gap: 8px; } .q-no { font-size: 17px; white-space: nowrap; margin-left: -15px; } .q-text { font-size: 18px; flex: 1; } .q-no, .q-text p { line-height: 30px; }

Q 10 : If the mean of the first n natural numbers is 15, then value of n is: .question-row { display: flex; align-items: flex-start; gap: 8px; } .q-no { font-size: 17px; white-space: nowrap; margin-left: -15px; } .q-text { font-size: 18px; flex: 1; } .q-no, .q-text p { line-height: 30px; }

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Q 4 :

The middle most observation of every data arranged in order is called

Q 10 :

If the mean of the first n natural numbers is 15, then value of n is: