Question

Compute quartile deviation from the following distribution of wages (in Rs.) of workers.
$\begin{tabular}{|l|c|c|c|c|c|} Wages (in Rs.) & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 \\ No. of workers & 22 & 38 & 46 & 35 & 20 \end{tabular}$

Answer 1

Answer:

3.59

Step-by-step explanation:

We know the formula: Qi = $l + \frac{h}{f} (\frac{iN}{4} - c) ; i = 1,2,3$

First Quartile: Q1 = $[\frac{iN}{4}th]value$ = (1 * 161)/4 = 40.25 th value.

Since it will be in the interval  (10 - 20), therefore, group of Q1 = (10 - 20)

Q1 = $10 + \frac{10}{38}(\frac{161}{4} - 22)$ = 14.80.

Third quartile will be:

Q3 = $3*\frac{161}{4} th value  = 120.75th$ value

120.75th value is in the interval (30 - 40).

Therefore, group for Q3 = (30 - 40).

Q3 = $30 + \frac{10}{35} (\frac{161}{4}-106)$ = 11.21

Quartile deviation = $\frac{14.8-11.21}{2}$ = 3.59