Which has more standard deviation?
Set 1 : {10, 20, 30, 40, 50} or
Set 2 : {1, 2, 3, 4, 5}

Set 1

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Set 2

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Equal

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Solution

The correct option is A Set 1
$Values of set 1 is 10 times that of set 2 . So, Mean of set 1 = 10 times mean of set 2 . Let x_{i} and ¯ x denote the elements and mean of set 1 respectively . And y_{i} and ¯ y denote the elements and mean of set 2 respectively . SD of set 1 = \sqrt{\frac{N \sum i = 1 {(x_{i} - ¯ x)}^{2}}{N}} = \sqrt{\frac{N 10^{2} \sum i = 1 {(y_{i} - ¯ y)}^{2}}{N}} = 10 \sqrt{\frac{N \sum i = 1 {(y_{i} - ¯ y)}^{2}}{N}} = 10 \times SD of set 2 Hence SD of set 1 is more .$

Suggest Corrections

Marks $(x)$	$10$	$20$	$30$	$40$	$50$
Number of students $(f)$	$4$	$3$	$6$	$5$	$2$

Class	$0 - 10$	$10 - 20$	$20 - 30$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$5$	$4$	$3$	$2$	$2$	$1$	$1$

Class:	1–10	10–20	20–30	30–40	40–50	50–60
Frequency:	11	29	18	4	5	3

Marks $(x)$	$10$	$20$	$30$	$40$	$50$
Number of students $(f)$	$4$	$3$	$6$	$5$	$2$

X	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
f	$10$	$8$	$15$	$8$	$4$