Question

Compute Q3, D6, P70 for the following data: 28, 17, 12, 25, 26, 19, 13, 27, 21, 16

Answer 1

Answer:

Q3 = 26.25        D6 = 23.4         P70 = 25.7

Step-by-step explanation:

Firstly arranging the data in ascending order we get,

  12, 13, 16, 17, 19, 21, 25, 26, 27, 28

• Q3 represent third quartile in the data.

The formula for calculating Q3 = $\frac{3(n+1)}{4} th$ observation where n is number  of observations in the data.

          Q3 = $\frac{3*(10+1)}{4} th$ obs. = 8.25th obs.

       8.25th obs = 8th obs + 0.25*(9th obs - 8th obs)

                          = 26 + 0.25*(27 - 26) = 26.25

   Therefore third quartile,Q3 = 26.25 .

• D6 represent sixth decile in the data.

  The formula for calculating D6 = $\frac{6(n+1)}{10} th$ obs.

                       = $\frac{6*(10+1)}{10} th$ obs. = 6.6th obs.

           6.6th obs = 6th obs + 0.6*(7th obs - 6th obs)

                            = 21 + 0.6*(25 - 21) = 23.4

     Therefore sixth decile,D6 = 23.4 .

• P70 represent 70th percentile in the data.

   The formula for calculating P70 = $\frac{70(n+1)}{100} th$ obs.

               P70 = $\frac{70*(10+1)}{100} th$ obs = 7.7th obs.

             7.7th obs = 7th obs + 0.7*(8th obs - 7th obs)

                              = 25 + 0.7*(26 - 25) = 25.7

        Therefore 70th percentile,P70 = 25.7 .

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Answer 2

Answer:

$Q3=26.25, D6=23.4, P70=25.7$

Step-by-step explanation:

Firstly arranging the data in ascending order we get,

$12,13,16,17,21,25,26,27,28$

$Q3$ represent third quartile in the data.

The formula for calculating $Q3=\frac{3(n+1)}{4}th$ observation where $n$ is number of observation in the data.

$Q3=\frac{3(10+1)}{4}th$ obs. $=8.25^{th} obs.$

$8.25^{th} obs=8^{th} obs+0.25(9^{th} obs-8^{th} obs)$

$=26+0.25(27-26)=26.25$

Therefore third quartile, $Q3=26.25$

$D6$ represent sixth decile in the data.

The formula for calculating $D6=\frac{6(n+1)}{10}th$ obs.

$=\frac{6(10+1)}{10}th$ obs. $=6.6^{th} obs.$

$6.6^{th}obs=6^{th} obs+0.6(7^{th}obs-6^{th} obs)$

$=21+0.6(25-21)=23.4$

Therefore sixth decile, $D6=23.4$

$P70$ represent $70^{th}$ percentile in the data.

The formula for calculating $P70= \frac{70(n+1)}{100}th$ obs.

$P70=\frac{70(10+1)}{100}th$ obs $=7.7^{th} obs.$

$7.7^{th} obs.=7^{th} obs. +0.7(8^{th} obs-7^{th} obs)$

$=25+0.7(26-25)=25.7$

Therefore, $70th$ percentile, $P70=25.7.$

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