Answer to Question #281818 in Statistics and Probability for Neha

Question

Find the quartile deviation for the following set of 11 bottles of 1 litre of emery milk for

11 days by a dealer.

34, 37, 32, 25, 40, 45, 50, 42, 39, 47, 55

7. Calculate the quartile deviation and its coefficient from the following:

x 43 44 45 46 47 48 49

f 10 18 21 18 15 10 8

Answer 1

6.

$$\def\arraystretch{1.5} \begin{array}{c:c:c} x & f & cf \\ \hline 25 & 1 & 1 \\ \hdashline 32 & 1 & 2 \\ \hdashline 34 & 1 & 3 \\ \hdashline 37 & 1 & 4 \\ \hdashline 39 & 1 & 5 \\ \hdashline 40 & 1 & 6 \\ \hdashline 42 & 1 & 7 \\ \hdashline 45 & 1 & 8 \\ \hdashline 47 & 1 & 9 \\ \hdashline 50 & 1 & 10 \\ \hdashline 55 & 1 & 11 \\ \hdashline \end{array}$$

Here, $n=11.$

$Q_1=(\dfrac{n+1}{4})$ th value of the observation

$=(\dfrac{11+1}{4})$ th value of the observation

$=(3)$ th value of the observation

$=34$

$Q_3=(\dfrac{3(n+1)}{4})$ th value of the observation

$=(\dfrac{3(11+1)}{4})$ th value of the observation

$=(9)$ th value of the observation

$=47$

Quartile deviation $=\dfrac{Q_3-Q_1}{2}=\dfrac{47-34}{2}=6.5$

7.

$$\def\arraystretch{1.5} \begin{array}{c:c:c} x & f & cf \\ \hline 43 & 10 & 10 \\ \hdashline 44 & 18 & 28 \\ \hdashline 45 & 21 & 49 \\ \hdashline 46 & 18 & 67 \\ \hdashline 47 & 15 & 82 \\ \hdashline 48 & 10 & 92 \\ \hdashline 49 & 8 & 100 \\ \hdashline \end{array}$$

Here, $n=100.$

$Q_1=(\dfrac{n+1}{4})$ th value of the observation

$=(\dfrac{100+1}{4})$ th value of the observation

$=(25.25)$ th value of the observation

$=44$

$Q_3=(\dfrac{3(n+1)}{4})$ th value of the observation

$=(\dfrac{3(100+1)}{4})$ th value of the observation

$=(75.75)$ th value of the observation

$=47$

Quartile deviation $=\dfrac{Q_3-Q_1}{2}=\dfrac{47-44}{2}=1.5$

Coefficient of Quartile deviation $=\dfrac{Q_3-Q_1}{Q_3+Q_1}=\dfrac{47-44}{47+44}=\dfrac{3}{91}\approx0.033$