Question

The production of electric bulbs in different factories is shown in the following table. Find the median of the productions.
No. of bulbs : No. of factories
produced (Thousands)
30-40 : 12
40-50 : 35
50-60 : 20
60-70 : 15
70-80 : 8
80-90 : 7
90-100 : 8

Answer 1

Step-by-step explanation:

$\begin{tabular}{|c|c|c|}</p><p>\cline{1-3}</p><p>Class interval & Frequency(fi) & \begin{tabular}[c]{@{}c@{}}Cumulative\\ Frequency\end{tabular} \\ \cline{1-3}</p><p>30-40 & 12 & 12 \\ \cline{1-3}</p><p>40-50 & 35 & 47 \\ \cline{1-3}</p><p>50-60 & 20 & 67 \\ \cline{1-3}</p><p>60-70 & 15 & 82 \\ \cline{1-3}</p><p>70-80 & 8 & 90 \\ \cline{1-3}</p><p>80-90 & 7 & 97 \\ \cline{1-3}</p><p>90-100 & 8 & 105 \\ \cline{1-3}</p><p>Total & & 105 \\ \cline{1-3}</p><p>\end{tabular}$

Median of grouped data:

$Median\:of\:grouped\:data=l + \bigg(\frac{ \frac{n}{2} - cf }{f} \bigg) \times h$

Here n= 105

$\frac{n}{2} = \frac{105}{2} = 52.5$

Median class:50-60

l= 50

h=10

f=20

cf=47

$50 + \bigg(\frac{ 52.5 - 47 }{20} \bigg) \times 10 \\ \\ \\ = > 50 + \frac{5.5}{20} \times 10 \\ \\ = > 50 + \frac{5.5}{2} \\ \\ = > 50 + 2.75 \\ \\ = 52.75$

Median= 52.75 bulbs

≈ 53 bulbs

Hope it helps you