Question
Find the Standard Deviation of the height of 100 students:
|
Height in inches |
Frequency |
|
Less than 62.5 |
5 |
|
Less than 65.5 |
23 |
|
Less than 68.5 |
65 |
|
Less than 71.5 |
92 |
|
Less than 74.5 |
100 |
Solution
First convert cumulative frequency with class interval.
Calculation of Standard Deviation
|
Height in Inches |
Frequency |
M.P. |
M–67 |
|
fd' |
fd'2 |
|
X |
(f) |
(m) |
d |
d' |
||
|
59.5-62.5 |
5 – 0 = 5 |
61 |
–6 |
–2 |
–10 |
20 |
|
62.5 – 65.5 |
23–5=18 |
64 |
–3 |
–1 |
–18 |
18 |
|
65.5 – 68.5 |
65–23 = 42 |
67 |
0 |
0 |
0 |
0 |
|
68.5 – 71.5 |
92–65 = 27 |
70 |
+3 |
+1 |
+27 |
27 |
|
71.5 – 74.5 |
100–92 = 8 |
73 |
+6 |
+2 |
+16 |
32 |
|
N = 100 |
Σfd'=15 |
Σfd'2 = 97 |
