Question

A softball team has played 10 games. The total runs scored in each game are shown below. 16, 8, 11, 14, 22, 24, 13, 9, 17, 22 Find the range, median, the first and third quartiles, and the interquartile range.

Answer 1

Answer:

__________ are the religious texts of Jains.

Answer 2

$\green{\large\underline{\bf{Solution-}}}$

Let first arrange the given data in ascending order :-

So we have,

8, 9, 11, 13, 14, 16, 17, 18, 22, 22, 24

Answer:- 1

We know,

Range = Largest Observation - Smallest Observation

$\red{\bf :\longmapsto\:Range = 24 - 8 = 16}$

Answer :- 2

Here, Number of observations, n = 10

So,

$\blue{\bf :\longmapsto\:Median = {\bigg(\dfrac{n + 1}{2} \bigg) }^{th} \: observation}$

${\rm :\longmapsto\:Median = {\bigg(\dfrac{10 + 1}{2} \bigg) }^{th} \: observation}$

${\rm :\longmapsto\:Median = {\bigg(\dfrac{11}{2} \bigg) }^{th} \: observation}$

${\rm :\longmapsto\:Median = {\bigg(5.5 \bigg) }^{th} \: observation}$

$\rm \: = \: \: {5}^{th} \: obs. \: + \: 0.5( {6}^{th} \: obs. - {5}^{th} \: obs.)$

$\rm \: = \: \: 14 + 0.5(16 - 14)$

$\rm \: = \: \: 14 + 0.5(2)$

$\rm \: = \: \: 14 +1$

$\rm \: = \: \: 15$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \blue{\boxed{{\bf\implies \:Median = 15}}}$

Answer :- 3

First Quartile

Here, Number of observations = 10

Thus,

$\green{\bf :\longmapsto\:Q_1 = {\bigg(\dfrac{n + 1}{4} \bigg) }^{th} \: observation}$

${\rm:\longmapsto\:Q_1 = {\bigg(\dfrac{10 + 1}{4} \bigg) }^{th} \: observation}$

${\rm:\longmapsto\:Q_1 = {\bigg(\dfrac{11}{4} \bigg) }^{th} \: observation}$

${\rm:\longmapsto\:Q_1 = {\bigg(2.75 \bigg) }^{th} \: observation}$

$\rm \: = \: \: {2}^{nd} \: obs. \: + \: 0.75( {3}^{rd} \: obs. - {2}^{nd} \: obs.)$

$\rm \: = \: \: 9 + 0.75(11 - 9)$

$\rm \: = \: \: 9 + 0.75(2)$

$\rm \: = \: \: 9 + 1.5$

$\rm \: = \: \: 10.5$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \green{\boxed{{\bf\implies \:Q_1 = 10.5}}}$

Answer :- 4

Third Quartile

Here, Number of observations, n = 10

Thus,

$\green{\bf :\longmapsto\:Q_3 = {\bigg(\dfrac{3(n + 1)}{4} \bigg) }^{th} \: observation}$

${\rm :\longmapsto\:Q_3 = {\bigg(\dfrac{3(10 + 1)}{4} \bigg) }^{th} \: observation}$

${\rm :\longmapsto\:Q_3 = {\bigg(\dfrac{3 \times (11)}{4} \bigg) }^{th} \: observation}$

${\rm :\longmapsto\:Q_3 = {\bigg(3 \times 2.75\bigg) }^{th} \: observation}$

${\rm :\longmapsto\:Q_3 = {\bigg(8.25\bigg) }^{th} \: observation}$

$\rm \: = \: \: {8}^{th} \: obs. \: + \: 0.25( {9}^{th} \: obs. - {8}^{th} \: obs.)$

$\rm \: = \: \: 22 + 0.25(22 - 22)$

$\rm \: = \: \: 22 + 0.25(0)$

$\rm \: = \: \: 22$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \green{\boxed{{\bf\implies \:Q_3 = 22}}}$

Answer :- 5

We know,

Inter-quartile Range is given by

$\red{\rm :\longmapsto\:Inter-quartile \: Range = Q_3 - Q_1 = 22 - 10.5 = 11.5}$