Page 115 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

Therefore, the mean score of the whole class is 56.67

To calculate the mean for the given distribution, we will use the formula for the mean of grouped data:
Mean = a + (Σfidi / Σfi)
Given data:

Number of Students Classmarks
Class di=xi - a fidi
(fi) (xi)
0-15 2 7.5 -30 -60

15-30 3 22.5 -15 -45

30-45 7 37.5=a 0 0

45-60 6 52.5 15 90

60-75 6 67.5 30 180

75-90 6 82.5 45 270

Σfi = 30 Σfidi = 435

Number of students: 2, 3, 7, 6, 6, 6
Classmarks (xi): 17.5, 32.5, 47.5, 62.5, 77.5, 92.5
di= xi - a
fidi: -60, -45, 0, 90, 180, 270
Σfi = 30
Σfidi = 435
Given mean= 62
Substitute the values into the formula: Mean= a+ (Σfidi / Σfi)
62=a+(435/30)
62 =a+ 14.5
62 - 14.5 =a
a= 37.5
Therefore, the value of ‘a’ is 37.5, and the mean of the distribution is 62.
Sample problems
1 What is the mean of the following numbers? 10, 39, 71, 39, 76, 38, 25.
2 What number would you divide by to calculate the mean of 3, 4, 5, and 6?
3 What measure of central tendency is calculated by adding all the values and dividing the sum by the number
of values?
4 The mean of four numbers is 71.5. If three of the numbers are 58, 76, and 88, what is the value of the fourth
number?
5 Determine the mean of the following set of numbers: 40, 61, 95, 79, 9, SO, 80, 63, 109,42
6 The mean weight of five complete computer stations is 167.2 pounds. The weights of four of the computer
stations are 158.4 pounds, 162.8 pounds, 165 pounds, and 178.2 pounds respectively. What is the weight of
the fifth computer station?

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CITS : WCS - Electrical - Exercise 9