Class 10 Maths Chapter 13 Question Answers - Statistics

Q11. Find the mean, mode and median of the following data:

Sol. Let the assumed mean ‘a’ = 35

Here, h =10

Classes	xi	fi	cf		fiui
0-10	5	3	3 + 0 = 3	-3	(-3) x 3 = -9
10-20	15	4	4 + 3 = 7	-2	(-2) x 4 = -8
20-30	25	7	7 + 7 = 14	-1	(-1) x 7 = -7
30-40	35	15	15 + 14 = 29	0	0 x 15 = 0
40-50	45	10	10 + 29 = 39	1	1 x 10 = 10
50-60	55	7	7 + 39 = 46	2	2 x 7 = 14
60-70	65	4	4 + 46 = 50	3	3 x 4 = 12
Total		∑fi = 50			∑uifi = 12

(i)

(ii) To find mode 
Here, greatest frequency = 15
∴ Modal class = 30 − 40
l = 30, f₁ = 15, f₀ = 7, f₂ = 10 and h = 10

So,
⇒  

(iii) To find median

Here, 
∴ Median class is 30−40.
Such that l = 30, cf = 14, f = 15 and h = 10

Q12. The following table gives daily income of 50 workers of a factory:

Find the mean, mode and median of the above data.

Sol. Let assumed mean a = 150. Here, h = 20

(i) Mean  

Thus, mean income is Rs 145.2

(ii) For finding the mode,
We have the greatest frequency = 14 which lies in the class 120−140
∴ Modal class = 120−140
Therefore, l = 120
f₁ = 14
f₀ = 12
f₂ = 8
and h = 20

(iii) For finding median,

And 25 lies in the class 120−140

Median class is 120−140

Since n/2 = 25, cf = 12, f = 14 and h = 20

 Median income = Rs138.57

Q13. Find the mode, median and mean for the following data:

Sol. Let the assumed mean a = 60. Here h = 10, we have:

(i)
⇒  
(ii) Median 

Here,  

∴ Median class is 45−55.

l = 45
cf = 38
f = 33 and h = 10

(iii) Mode: Greatest frequency is 33 which corresponds to the class 45−55.

l = 45,  h = 10
f₁ = 33,  f2 = 17
f₀ = 31

Q14. A survey regarding the heights (in cm) of 50 girls of Class X of a school was conducted and the following data was obtained:

Find the mean, median and mode of the above data.

Sol. We have:

(i)  

(ii) ∵    

∴ Median class is 150−160.
∴ We have,
l = 150
f = 20
cf = 2
2h = 10

∴  
⇒  

(iii) ∵ Greatest frequency = 20
∴ Modal class = 150−160

So, we have

l = 150, f₀ = 12, f₁ = 20
f₂ = 8 and h = 10

Q15. Find the mean, mode and median of the following data:

 
Sol. 

(i) Mean:

Let the assumed mean ‘a’ = 35

Now we have the following data:

Class	Class mark xi	fi	Cf		fiui
0-10	5	5	5 + 0 = 5	-3	(-3) x 5 = -15
10-20	15	10	5 + 10 = 15	-2	(-2) x 10 = -20
20-30	25	18	15 + 18 = 33	-1	(-1) x 18 = -18
30-40	35	30	33 + 30 = 63	0	0 x 30 = 0
40-50	45	20	63 + 20 = 93	1	1 x 20 = 20
50-60	55	12	83 + 12 = 95	2	2 x 12 = 24
60-70	65	5	95 + 5 = 100	3	3 x 5 = 15

 
Here ∑f_i = 100 and ∑f_iu_i = 6

(ii) Mode:

Here, the maximum frequency is 30.
∴ Modal class is 30−40.
So, we have

l = 30, h = 10
f₁ = 30,
f₀ = 18
f₂ = 20

(iii) Median: 

∴ Median class = 30−40
So, we have:

l = 30, h = 10, cf = 33, f = 30

Q16. Find the mean, mode and median for the following data:

Sol. Let the assumed mean = 35;  h = 10

Classes	xi	fi	cf		fiui
0-10	5	3	3 + 0 = 3	-3	(-3) x 3 = -9
10-20	15	8	3 + 8 = 11	-2	(-2) x 8 = -16
20-30	25	10	11 + 10 = 21	-1	(-1) x 10 = -10
30-40	35	15	21 + 15 = 36	0	0 x 15 = 0
40-50	45	7	36 + 7 = 43	1	1 x 7= 7
50-60	55	4	43 + 4 = 47	2	2 x 4= 8
60-70	65	3	47 + 3 = 50	3	3 x 3= 9
Total		∑fi = 50			∑fiui= -11

Now,

(i)

(ii) To find mode 
Here, highest frequency is 15.
∴ Modal class is 30−40.

Here,

l = 30, f₁ = 15, f₀ = 10
f₂ = 7 and h = 10

(iii) ∵  

So, the median class is 30−40.

∴ We have l = 30, cf = 21, f = 15 and h = 10

We have