Question

The class mark and frequency of a data is given in the graph. From the graph, Find:

1. the table showing the class interval and frequency. 
2. the mean.

Answer 1

a. Table showing class interval and frequency

To find the class intervals, we determine the class size (h) by calculating the difference between consecutive class marks:

h = 15 – 13 = 2.

Since the class size is 2, each class interval will extend 1 unit below and 1 unit above its class mark calculated as `x ± h/2`.

Class Mark (x)	Class Interval	Frequency (f)
13	12 – 14	8
15	14 – 16	2
17	16 – 18	3
19	18 – 20	4
21	20 – 22	5
23	22 – 24	6
Total		Σf = 28

b. Finding the mean

The mean `(barx)` for grouped data is calculated using the formula:

`barx = (sum(f xx x))/(sumf)`

Step 1: Calculate the product of class marks and frequencies (f × x):

8 × 13 = 104

2 × 15 = 30

3 × 17 = 51

4 × 19 = 76

5 × 21 = 105

6 × 23 = 138

Step 2: Sum the values:

Σ(f × x) = 104 + 30 + 51 + 76 + 105 + 138 = 504

Σf = 8 + 2 + 3 + 4 + 5 + 6 = 28

Step 3: Solve for mean:

`barx = 504/28`

`barx` = 18

The mean of the data is 18.