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Question : Calculate the mean from the following table.

Scores Frequencies
0-10 2
10-20 4
20-30 12
30-40 21
40-50 6
50-60 3
60-70 2

Option 1: 33.4

Option 2: 32.6

Option 3: 35.8

Option 4: 34.2


Team Careers360 16th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: 33.4


Solution : The formula for the mean ($X$) using the method of assumed mean is:
$X = A + \frac{\sum fd}{\sum f}$ where $A$ is assumed mean, $f$ is frequency, and $d$ is deviation from mean.
The assumed mean ($A$) is usually taken as the midpoint of the middle class. In this case, it's 35.
The midpoints of the score ranges are 5, 15, 25, 35, 45, 55, and 65.
The frequencies are 2, 4, 12, 21, 6, 3, and 2.

Midpoint ($x$) Frequency($f$) Deviation ($d = x - A$) $fd$
5 2 –30 –60
15 4 –20 –80
25 12 –10 –120
35 21 0 0
45 6 10 60
55 3 20 60
65 2 30 60
$\sum f$ = 50 $\sum fd$ = –80

The formula for the mean ($X$) using the method of assumed mean is:
$X = A + \frac{\sum fd}{\sum f}$
⇒ $X = 35 + \frac{-80}{50} = 33.4$
Hence, the correct answer is 33.4.

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