Question

The scores in Mathematics Test (out of 30) of 15 students 27, 30, 16, 23, 24, 15, 29, 14, 16, 13, 10, 16, 16, 26, 25 Find: a) Mean b) Median c) Mode d) Range​

Answer 1

ans

a. mean

20

b. median

8th

c.mode

16

d. range

20

Answer 2

$\large\underline{\sf{Solution-}}$

Given data is

27, 30, 16, 23, 24, 15, 29, 14, 16, 13, 10, 16, 16, 26, 25

Now,

Sum of observations = 27 + 30 + 16 + 23 + 24 + 15 + 29 + 14 + 16 + 13 + 10 + 16 + 16 + 26 + 25 = 300

Number of observations = 15

We know

$\boxed{\tt{ Mean = \frac{Sum \: of \: observations}{Number \: of \: observations} \: }}$

So, on substituting the values, we get

$\rm \implies\:Mean = \dfrac{300}{15}$

$\rm \implies\:\boxed{\tt{ Mean \: = \: 20 \: }}$

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Given data is

27, 30, 16, 23, 24, 15, 29, 14, 16, 13, 10, 16, 16, 26, 25

Now, arrange the data in ascending order, we get

10, 13, 14, 15, 16, 16, 16, 16, 23, 24, 25, 26, 27, 29, 30

Number of observations, n = 15 which is odd

So,

$\boxed{\tt{ Median \: = \: {\bigg[\dfrac{n + 1}{2} \bigg]}^{th} \: observations \: }}$

$\rm :\longmapsto\: Median \: = \: {\bigg[\dfrac{15 + 1}{2} \bigg]}^{th} \: observations \:$

$\rm :\longmapsto\: Median \: = \: {\bigg[\dfrac{16}{2} \bigg]}^{th} \: observations \:$

$\rm :\longmapsto\: Median \: = \: {\bigg[8 \bigg]}^{th} \: observations \:$

$\bf\implies \:Median = 16$

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Given data is

27, 30, 16, 23, 24, 15, 29, 14, 16, 13, 10, 16, 16, 26, 25

Now, arrange the data in ascending order, we get

10, 13, 14, 15, 16, 16, 16, 16, 23, 24, 25, 26, 27, 29, 30

We know

Mode is defined as that number which repeat maximum number of times.

Since, 16 repeat 4 times.

$\bf\implies \:Mode \: = \: 16$

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Given data is

27, 30, 16, 23, 24, 15, 29, 14, 16, 13, 10, 16, 16, 26, 25

Now, arrange the data in ascending order, we get

10, 13, 14, 15, 16, 16, 16, 16, 23, 24, 25, 26, 27, 29, 30

Range is defined as difference of highest and lowest value in given set of observations.

Here,

Lowest value = 10

Highest value = 30

So, Range = Highest value - Lowest value

$\rm \implies\:Range = 30 - 10$

$\bf \implies\:Range = 20$

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