Question

10. Median life time of bulbs is 980 hours, find the missing frequencies in the following frequency distribution, when it is given that sum of all frequencies is 80. Life time (in hours) No of bulbs 700 - 800 8 800 - 900 x 900 - 1000 30 1000 - 1100 14 1100 - 1200 10 1200 - 1300 y 1300 - 1400 4

Answer 1

Step-by-step explanation:

Given:Median 980 hours

To find:Find the missing frequencies

Solution:

To find the missing frequencies firstly draw the cumulative frequency table

$\begin{tabular}{|c|c|c|}\cline{1-3}Class\:interval&frequency&Cumulative\: Frequency\\\cline{1-3}700-800&8&8\\\cline{1-3}800-900&x&8+x\\\cline{1-3}900-1000&30&38+x\\\cline{1-3}1000-1100&14&52+x\\\cline{1-3}1100-1200&10&62+x\\\cline{1-3}1200-1300&y&62+x+y\\\cline{1-3}1300-1400&4&66+x+y\\\cline{1-3}Total&80&\\\cline{1-3}\end{tabular}$

FORMULA OF MEDIAN:

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

As Median of data is 980,thus from median it is clear that median class is 900-1000

Thus,

l=900

CF=8+x

f=30

n/2=40

h=100

Put these values into formula,and find the unknown frequency

$980=900+\frac{40-8-x}{30}\times\:100\\\\80=\frac{32-x}{3}\times\:10\\\\ 8=\frac{32-x}{3}\\\\24=32-x\\\\24-32=-x\\\\-8=-x\\\\\bold{x=8}$

Sum of all frequencies are 80,thus

66+x+y=80

Put the value of x

66+8+y=80

74+y=80

y=6

Thus,

Missing frequencies are x=8 and y=6.

Hope it helps you.

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