Chapter 9: Statistics (Exercise 9.2)
Chapter 9: Statistics (Exercise 9.2)
Question 1:
Weights of parcels in a transport office are given below. Find the mean weight of the parcels.
* Weight (in kg): 50, 65, 75, 90, 110, 120
* No. of parcels (f): 25, 34, 38, 40, 47, 16
Solution:
* Calculating f × x for each observation:
- 50 × 25 = 1250
- 65 × 34 = 2210
- 75 × 38 = 2850
- 90 × 40 = 3600
- 110 × 47 = 5170
- 120 × 16 = 1920
* Total frequency (Σf) = 25 + 34 + 38 + 40 + 47 + 16 = 200
* Sum of products Σ(f × x) = 1250 + 2210 + 2850 + 3600 + 5170 + 1920 = 17000
Mean = Σ(f × x) / Σf = 17000 / 200 = 85 kg
Question 2:
Number of families in a village in correspondence with the number of children are given below. Find the mean number of children per family.
* No. of children (x): 0, 1, 2, 3, 4, 5
* No. of families (f): 11, 25, 32, 10, 4, 2
Solution:
* Calculating f × x:
- 0 × 11 = 0
- 1 × 25 = 25
- 2 × 32 = 64
- 3 × 10 = 30
- 4 × 4 = 16
- 5 × 2 = 10
* Σf = 11 + 25 + 32 + 10 + 4 + 2 = 84
* Σ(f × x) = 0 + 25 + 64 + 30 + 16 + 10 = 145
Mean = 145 / 84 = 1.73 children per family
Question 3:
If the mean of the following frequency distribution is 7.2, find the value of K.
* x: 2, 4, 6, 10, 12
* f: 4, 7, 10, K, 9
Solution:
* Calculating f × x:
- 2 × 4 = 8
- 4 × 7 = 28
- 6 × 10 = 60
- 10 × K = 10K
- 12 × 9 = 108
* Σf = 4 + 7 + 10 + K + 9 = 30 + K
* Σ(f × x) = 8 + 28 + 60 + 10K + 108 = 204 + 10K
Given Mean = 7.2:
(204 + 10K) / (30 + K) = 7.2
204 + 10K = 7.2 × (30 + K)
204 + 10K = 216 + 7.2K
10K - 7.2K = 216 - 204
2.8K = 28
K = 10
Question 4:
Number of villages with respect to their population (in thousands) as per India census 2011 are given below. Find the mean population per village.
* Population in thousands (x): 12, 5, 18, 25, 30
* No. of villages (f): 20, 15, 25, 10, 5
Solution:
* Calculating f × x:
- 12 × 20 = 240
- 5 × 15 = 75
- 18 × 25 = 450
- 25 × 10 = 250
- 30 × 5 = 150
* Σf = 20 + 15 + 25 + 10 + 5 = 75
* Σ(f × x) = 240 + 75 + 450 + 250 + 150 = 1165
Mean = 1165 / 75 = 15.533 thousand = 15,533 people per village