Question

Rank each of the following value in order of smallest to largest: (7)

I. the upper quartile.

II. the median.

III. the 20th percentile.

IV. decile 6.

V. the 0.38 fractile.

VI. the 70th percentile.

VII. the lower quartile

Answer 1

Let 'N' be the no. of bservation

then,

Upper Quartile, $Q_3=\dfrac{3N}{4}=0.75N$

Median, $Q_2=\dfrac{N}{2}=0.5N$

$20^{th}$ ​Percentile,$P_{20}=\dfrac{20N}{100}=0.2N$

Decile 6, $D_6=\dfrac{6N}{10}=0.6N$

0.38 fractile, $F_{0.38}=0.38N$

$70^{th}$ ​Percentile,$P_{70}=\dfrac{70N}{100}=0.70N$

Lower Quartile, $Q_1=\dfrac{N}{4}=0.25N$

From the above results, The ranks from smallest value to largest value are as follows-

(1) $20^{th}$ Percentile

(2) Lower Quartile

(3) 0.38 fractile

(4) Median

(5) Decile 6

(6) $70^{th}$ Percentile

(7) Upper Quartile