Question

Find the mean, median, mode, and range of the following groups:
(a) 2, 4, 6, 7, 9, 7, 4, 6, 8, 10, 7, 14​

Answer 1

Solution :

We know that ,

$\large \sf\fbox{ \fbox{Mean = \frac{Sum \: of \: all \: the \: observation }{Total \: number \: of \: observation} }}$

$\sf = \frac{2 + 4 + 6 + 7 + 9 + 7 + 4 + 6 + 8 + 10 + 7 + 14}{12} \\ \\ \sf = \frac{84}{12} \\ \\\sf = 3$

Thus , the mean is 3

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Arranging the data in ascending order

2 , 4 , 4 , 6 , 6 , 7 , 7 , 7 , 8 , 9 , 10 , 14

We know that , if n is an even number ,

$\sf \large \fbox{ \fbox{Median = Mean \: of \: the \: values \: of \: the {( \frac{n}{2} )}^{th} \: and \: {( \frac{n}{2} + 1)}^{th} }}$

There are 12 terms , So there are two middle terms i.e the $\sf {(\frac{12}{2})}^{th} \ \: and \: { (\frac{12}{2} + 1)}^{th}$ i.e the 6th and 7th terms

So , the median is the mean values of the 6th and 7th terms i.e

$\sf \implies Median = \frac{7 + 7}{2} \\ \\ \sf \implies Median = \frac{14}{2} \\ \\ \sf \implies Median = 7$

Thus , the median is 7

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We arrange this data in the following form :

2 , 4 , 4 , 6 , 6 , 7 , 7 , 7 , 8 , 9 , 10 , 14

Here 7 occurs most frequently , i.e., 3 times

Thus , the mode is 7

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We know that ,

$\large \sf\fbox{ \fbox{Range = Largest \: number - Smallest \: number }}$

$\sf = 14 - 2 \\ \\ \sf = 12$

Thus , the range is 12