Question

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

a)The upper quartile

b)The median

c)The 20th percentile

d)Decile 6

e)The 0.38 fractile

f)The 70th percentile

g)The lower quartile

Answer 1

Let number of observations = N

Then,

First we calculate all of these and then arrange accordingly

So,

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

Median $Q_2=\dfrac{1}{2}N=0.5N$

20th percentile $P_{20}=\dfrac{20}{100}N=0.2N$

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

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

70th percentile $P_{70}=\dfrac{70}{100}N=0.70N$

Lower Quartile, $Q_1=\dfrac{1}{4}N=0.25N$

From the above results, now arrange from smallest to largest

(1) $20^{th}$ Percentile

(2) Lower Quartile

(3) 0.38 fractile

(4) Median

(5) Decile 6

(6) $70^{th}$ Percentile

(7) Upper Quartile