Question

Find 'mean' and 'mode' of the following data:

| Class | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 | 40-45 |
|---|---|---|---|---|---|---|
| Frequency | 6 | 16 | 17 | 4 | 5 | 2 |

Approach

Using assumed mean method with $A = 27.5$ , mean = $27.5 - \frac{8}{50} \times 5 = 26.7$ . Modal class 25-30. Mode = $25 + 5 \times \frac{17 - 16}{34 - 16 - 4} = 25.36$ .

Step-by-step working

1
Prepare frequency table with class marks and deviations
1.5 marks
2
Compute mean using $\overset{x}{ˉ} = A + \frac{\sum f _{i} u _{i}}{\sum f _{i}} \times h = 26.7$
1.5 marks
3
Identify modal class 25-30
0.5 marks
4
Apply mode formula to get 25.36
1.5 marks

Concepts used

meanmodegrouped dataassumed mean method

Approach

Step-by-step working

Concepts used

Similar question types