Statistics class 10 questions with solutions

Q 11 :

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 of every data arranged in order is called median.

Q 12 :

The median of a given frequency distribution is found graphically with the help of:

Frequency curve
Bar graph
Histogram
An ogive

1

2

3

4

(4)

An ogive is a plot of the cumulative frequencies of a frequency distribution.
When the cumulative frequencies of class-intervals are plotted against upper or lower limits of class intervals, the graph obtained by joining the points by free hand forming smooth curve is called the cumulative frequency curve or ogive.
Ogive graphs are used to find the median of the given set of data.

Q 13 :

The median of the following observations given in order 16, 18, 20, 24 − x, 22 + 2x, 28, 30, 32 is 24. The value of x is:

5
4
2
1

1

2

3

4

(3)

Given, median of the data 16, 18, 20, 24 − x, 22 + 2x, 28, 30, 32 is 24.

$H e r e, n = 8 (E v e n) ∴ Median = \frac{{(\frac{n}{2})}^{th} observation + {(\frac{n}{2} + 1)}^{th} observation}{2} 24 = \frac{4th observation + 5th observation}{2} \Rightarrow 48 = (24 - x) + (22 + 2 x) \Rightarrow 48 = 46 + x \Rightarrow x = 2 H e n c e, t h e v a l u e o f x i s 2 .$

Q 14 :

The mean and median of $a, b a n d c a r e$ 50 and 35, respectively, where $a < b < c .$ $I f c - a = 55, t h e n :$

(i) b - a = 10 (ii) a + c = 115 (iii) a = 20 (iv) b = 35

Choose the correct option from the following:

(i) and (iii)
(ii) and (iii)
(i) and (iv)
(ii) and (iv)

1

2

3

4

(4)

$S i n c e a < b < c Median = b \Rightarrow b = 35 Mean = \frac{a + b + c}{3} = 50 \Rightarrow a + b + c = 150 \Rightarrow a + c = 150 - 35 = 115 ∴ (ii) is correct. G i v e n, a + c = 115 c - a = 55 \Rightarrow a = 30 and c = 85 \Rightarrow b - a = 35 - 30 = 5 ∴ Option (d) is correct.$

Q 15 :

The empirical relation between the mode, median and mean of a distribution is:

Mode = 3 Median − 2 Mean
Mode = 3 Mean − 2 Median
Mode = 2 Median − 3 Mean
Mode = 2 Mean − 3 Median

1

2

3

4

(1)

We know that the empirical relation is given by,

Mode = 3 Median − 2 Mean

Q 16 :

Using the empirical formula, the mode of a distribution whose mean is 8.32 and the median is 8.05, is equal to:

7.51
7.21
7.01
7.31

1

2

3

4

(1)

Given, mean = 8.32 and median = 8.05

∴ Mode = 3 × Median − 2 × Mean

= 3 × 8.05 − 2 × 8.32
= 24.15 − 16.64
= 7.51

Q 17 :

The times in seconds, taken by 150 athletes to run a 110 m hurdle race are tabulated below:

Class 13.8–14 14–14.2 14.2–14.4 14.4–14.6 14.6–14.8 14.8–15

Frequency 2 4 5 71 48 20

The number of athletes who completed the race in or equal to 14.6 seconds is:

Class	13.8–14	14–14.2	14.2–14.4	14.4–14.6	14.6–14.8	14.8–15
Frequency	2	4	5	71	48	20

11
71
82
130

1

2

3

4

(3)

We have,

Class	Frequency	Cumulative frequency
13.8–14	2	2
14–14.2	4	6
14.2–14.4	5	11
14.4–14.6	71	82
14.6–14.8	48	130
14.8–15	20	150

From the above cumulative frequency table, 82 athletes completed the race in or equal to 14.6 seconds.

Q 18 :

If the mode of the following data is K, then the value of K in the data set
9, 8, 6, 7, 1, 6, 10, 6, 7, K² − 12K + 42, 9, 7 and 13 is:

(i) 6 (ii) 9 (iii) 7 (iv) 13

Choose correct option from the following:

(iii) and (iv)
(i) and (iii)
Only (i)
(i) and (ii)

1

2

3

4

(2)

In the above dataset, value 6 and 7 have occurred most number of times, i.e., 3 times.

Also, mode = K.

So, either 6 or 7 would be the mode.

If K = 6,
$K ² - 12 K + 42 = 6 ² - 12 (6) + 42 = 6$

If K = 7,
$K ² - 12 K + 42 = 7 ² - 12 (7) + 42 = 7$

∴ K = 6 and K = 7

So, (i) and (iii) are correct.

Topic Question Set

Q 11 :

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

Q 12 :

The median of a given frequency distribution is found graphically with the help of:

Q 13 :

The median of the following observations given in order 16, 18, 20, 24 − x, 22 + 2x, 28, 30, 32 is 24. The value of x is:

Q 14 :

The mean and median of $a, b a n d c a r e$ 50 and 35, respectively, where $a < b < c .$ $I f c - a = 55, t h e n :$

(i) b - a = 10 (ii) a + c = 115 (iii) a = 20 (iv) b = 35

Choose the correct option from the following:

Q 15 :

The empirical relation between the mode, median and mean of a distribution is:

Q 16 :

Using the empirical formula, the mode of a distribution whose mean is 8.32 and the median is 8.05, is equal to:

Q 17 :

The times in seconds, taken by 150 athletes to run a 110 m hurdle race are tabulated below:

Class 13.8–14 14–14.2 14.2–14.4 14.4–14.6 14.6–14.8 14.8–15

Frequency 2 4 5 71 48 20

The number of athletes who completed the race in or equal to 14.6 seconds is:

Q 18 :

If the mode of the following data is K, then the value of K in the data set
9, 8, 6, 7, 1, 6, 10, 6, 7, K² − 12K + 42, 9, 7 and 13 is:

(i) 6 (ii) 9 (iii) 7 (iv) 13

Choose correct option from the following:

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Topic Question Set

Q 11 : 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 15 : The empirical relation between the mode, median and mean of a distribution 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 11 :

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

Q 15 :

The empirical relation between the mode, median and mean of a distribution is: