Question

Find the standard deviation for the grouped data.

College Units
0-9
10-19
20-29
30-39
40-49
50-59
Frequency
4
3
6
3
5
9

Answer 1

The standard deviation is 16.08.

Explanation:

Mid point, (0+9)/2=4.5

(10+19)/2=14.5

(20+29)/2=24.5

(30+39)/2=34.5

(40+49)/2=44.5

(50+59)/2=54.5

Mean = [(4×4.5)+(3×14.5)+(6×24.5)+(3×34.5)+(5×44.5)+(9×54.5)] / (4+3+6+3+5+9)

Mean = (18+43.5+147+103.5+222.5+490.5) / 30

= 1025 / 30

Mean = 34.17

Sum of square deviation= 1106.81+914.79+634.14+0.9192+1099.25+3783.41

= 7749.41

Standard deviation= √(7749)/30

=√258.3137

= 16.08