Concept:The arithmetic mean for grouped data is the sum of (midpoint of each class times its frequency) divided by total frequency.Explanation:First, find the midpoints (xi​) for each class: 5-15 midpoint = 10, 15-25 midpoint = 20, 25-35 midpoint = 30, 35-45 midpoint = 40.Multiply each midpoint by its frequency (fi​):
Class Interval
f_{i}
x_{i}
x_{i}f_{i}
5 – 15
20
10
200
15 – 25
30
20
600
25 – 35
30
30
900
35 – 45
20
40
800
Total
∑f_{i}=100
2500
Add all frequencies: 20+30+30+20=100.Add all xi​fi​: 200+600+900+800=2500.Mean = ∑fi​∑xi​fi​​=1002500​=25.Answer:B. 25