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
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.
