Question

Find 'mean' and 'mode' of the following data : Frequency Distribution Table

Class	0 – 15	15 – 30	30 – 45	45 – 60	60 – 75	75 – 90
Frequency	11	8	15	7	10	9

Answer 1

Given Data:

Class	0–15	15–30	30–45	45–60	60–75	75–90
Frequency (f)	11	8	15	7	10	9
Mid-value (x)	7.5	22.5	37.5	52.5	67.5	82.5
f × x	82.5	180	562.5	367.5	675	742.5

Step 1: Calculate total frequency and total of f × x
\[ \sum f = 11 + 8 + 15 + 7 + 10 + 9 = 60 \] \[ \sum f x = 82.5 + 180 + 562.5 + 367.5 + 675 + 742.5 = 2610 \]

Step 2: Calculate mean
\[ \bar{x} = \frac{\sum f x}{\sum f} = \frac{2610}{60} = 43.5 \]

Step 3: Find modal class
The highest frequency is 15, corresponding to class 30–45.

Step 4: Calculate mode using formula
\[ \text{Mode} = l + \frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)} \times h \] Where:
 

• \(l = 30\) (lower limit of modal class)
• \(f_1 = 15\) (frequency of modal class)
• \(f_0 = 8\) (frequency before modal class)
• \(f_2 = 7\) (frequency after modal class)
• \(h = 15\) (class width)

Substitute values:
\[ \text{Mode} = 30 + \frac{15 - 8}{(2 \times 15) - 8 - 7} \times 15 = 30 + \frac{7}{30 - 15} \times 15 = 30 + \frac{7}{15} \times 15 = 30 + 7 = 37 \]

Final Answer:
\[ \text{Mean} = 43.5, \quad \text{Mode} = 37 \]