Find the mean and the mode for the following data : Class Frequency 5-10 5 10-15 6 15-20 15 20-25 10 25-30 5 30-35 4…

Ans.
class
$x_i$
$f_i$
$u_i$
$f_iu_i$
5-10
7.5
5
-3
-15
10-15
12.5
6
-2
-12
15-20
17.5
15
-1
-15
20-25
$a = 22.5$
10
0
0
25-30
27.5
5
1
5
30-35
32.5
4
2
8
35-40
37.5
2
3
6
40-45
42.5
2
4
8
Total
49
-15
Correct table (1
frac{1}{2} Mark)
Mean = $22.5 + \frac{(-15)}{49} \times 5$ (1 Mark)
$= 20.97$ (1/2 Mark)
Modal class: 15 - 20 (1 Mark)
Mode = $15 + \frac{(15-6)}{30-6-10} \times 5$ (1
frac{1}{2} Mark)
$= 18.2$ (1/2 Mark)