Question

if minimum is "-2" first quartile is 7 median is 15 third quartile is 21 maximum is 24 then coefficient of quartile is?​

Answer 1

Answer:

The coefficient of quartile is 0.5.

Concept:

Statistics: Quartile Deviation and Range.

Given:

Minimum of the observations, S = -2

Maximum of the observations, L = 24

First Quartile, Q₁ = 7

Third Quartile, Q₃ = 21

Median, M = 15

Find:

The coefficient of Quartile or Quartile deviation.

Solution:

Range of the series, R = L-S

where L = Maximum of the observations

S = Minimum of the observations

      R  = 24 - (-2)

           = 24 + 2 = 26

Coefficient of range = (L-S)/(L+S)

                                  = (24 + 2)/(24-2)

                                  = 26/22

                                  = 1.18

Coefficient of quartile deviation = $\frac{Q_3-Q_1}{Q_3 + Q_1}$

Q₃ = Third quartile of the series

Q₁ = First quartile of the series

                                $= \frac{21 - 7}{21 + 7}\\\\= \frac{14}{28} \\\\=\frac{1}{2} \\= 0.5$

Hence, the Coefficient of quartile deviation = 0.5.

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Answer 2

Answer:

$0.5$

Step-by-step explanation:

We will use the concepts of "Quartile Deviation and Range" in the given question.

Given:

We have been given that:

• The minimum of the observations, i.e., $S$ is $-2$.
• The maximum of the observations, i.e., $L$ is $24$.
• The first Quartile, i.e., $Q_{1}$ is $7$.
• The third Quartile, i.e., $Q_{3}$ is $21$.
• The median, i.e., $M$ is $15$.

To Find:

We have to find the coefficient of Quartile or Quartile deviation.

Solution:

We know that the range is equal to the difference between the highest value and the lowest value.

Here, the coefficient of quartile = $\frac{Q_{3} -Q_{1} } {Q_{3}+Q_{1} } }$

= $\frac{21-7}{21+7}$

= $\frac{14}{28}$

= $\frac{1}{2}$

= $0.5$

Hence, the coefficient of the quartile is $0.5$.

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