Calculate the standard deviation from the following frequency distribution.
C.I. $60 - 62$ $62 - 64$ $64 - 66$ $66 - 68$ $68 - 70$
Frequency $35$ $27$ $20$ $13$ $5$

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Solution

$M e a n = \frac{\sum x_{i} f_{i}}{\sum f_{i}}$
$= \frac{6352}{100}$
$= 63.52$
$\Rightarrow S . D = \sqrt{∣ ∣ ∣ ∣ \frac{\sum f_{i} x_{1}^{2}}{\sum f_{i}} - {(m e a n)}^{2} ∣ ∣ ∣ ∣}$
$= \sqrt{5.8096}$
$= 2.4103$
Hence, the answer is $2.4103.$

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Q. Heights (in inches) of 35 students of a class in given below. Classify the following data in a discrete frequency series

58	60	72	68	58	55	58	72	55	68	66	60
60	55	76	66	58	72	68	60	55	68	55	58
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$\begin{matrix} 95 & 92 & 91 & 90 & 88 & 82 & 86 & 87 & 87 & 88 & 70 & 72 & 76 & 77 & 77 79 & 79 & 79 & 78 & 78 & 68 & 67 & 67 & 66 & 65 & 62 & 62 & 62 & 62 & 64 58 & 59 & 60 & 60 & 60 & 60 & 61 & 62 & 62 & 62 & 55 & 55 & 55 & 56 & 57 54 & 53 & 52 & 52 & 50 \end{matrix}$

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C.I.	$60 - 62$	$62 - 64$	$64 - 66$	$66 - 68$	$68 - 70$
Frequency	$35$	$27$	$20$	$13$	$5$

58	60	72	68	58	55	58	72	55	68	66	60
60	55	76	66	58	72	68	60	55	68	55	58
62	66	72	58	60	68	55	58	65	72	68

58	60	72	68	58	55	58	72	55	68	66	60
60	55	76	66	58	72	68	60	55	68	55	58
62	66	72	58	60	68	55	58	65	72	68

Calculate the standard deviation from the following frequency distribution.C.I.60−6262−6464−6666−6868−70Frequency352720135

Mean=∑xifi∑fi =6352100 =63.52⇒S.D= ⎷∣∣ ∣∣∑fix21∑fi−(mean)2∣∣ ∣∣ =√5.8096 =2.4103Hence, the answer is 2.4103.

Calculate the standard deviation from the following frequency distribution.
C.I. $60 - 62$ $62 - 64$ $64 - 66$ $66 - 68$ $68 - 70$
Frequency $35$ $27$ $20$ $13$ $5$

$M e a n = \frac{\sum x_{i} f_{i}}{\sum f_{i}}$
$= \frac{6352}{100}$
$= 63.52$
$\Rightarrow S . D = \sqrt{∣ ∣ ∣ ∣ \frac{\sum f_{i} x_{1}^{2}}{\sum f_{i}} - {(m e a n)}^{2} ∣ ∣ ∣ ∣}$
$= \sqrt{5.8096}$
$= 2.4103$
Hence, the answer is $2.4103.$

58	60	72	68	58	55	58	72	55	68	66	60
60	55	76	66	58	72	68	60	55	68	55	58
62	66	72	58	60	68	55	58	65	72	68