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13.Statistics
medium
What is the standard deviation of the following series
|
class |
0-10 |
10-20 |
20-30 |
30-40 |
|
Freq |
1 |
3 |
4 |
2 |
A
$81$
B
$7.6$
C
$9$
D
$2.26$
Solution
(c)
|
$Class$ |
$f_i$ |
$y_i$ |
$d = {y_i} – A$ $A = 25$ |
$f_id_i$ |
$f_id_i^2$ |
|
$0-10$ |
$1$ |
$5$ |
$-20$ |
$-20$ |
$400$ |
|
$10-20$ |
$3$ |
$15$ |
$-10$ |
$-30$ |
$300$ |
|
$20-30$ |
$4$ |
$25$ |
$0$ |
$0$ |
$0$ |
|
$30-40$ |
$2$ |
$35$ |
$10$ |
$20$ |
$200$ |
|
$Total$ |
$10$ |
|
|
$-30$ |
$900$ |
${\sigma ^2} = \frac{{\sum {f_i}d_i^2}}{{\sum {f_i}}} – {\left( {\frac{{\sum {f_i}{d_i}}}{{\sum {f_i}}}} \right)^2}$
$= \frac{{900}}{{10}} – {\left( {\frac{{ – 30}}{{10}}} \right)^2}$
${\sigma ^2} = 90 – 9 = 81$
==> $\sigma$ = $9$.
Standard 11
Mathematics
