The lifetimes of 100 light bulbs are tabulated below- Find the median lifetime- t e x t L i f e t i m e i n h o u r s - Frequency INhline Whline Whline Whline Whine Whine WhlineMhine array A- 68-3 hoursB- 71-1 hoursC- 75-6 hoursD- 81-4 hours

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Standard XI

Statistics

Median of Continuous Series

The lifetimes...

Question

The lifetimes of 100 light bulbs are tabulated below. Find the median lifetime.

$\begin{matrix} Lifetime (in hours) & Frequency 0 - 20 & 7 20 - 40 & 13 40 - 60 & 20 60 - 80 & 18 80 - 100 & 16 100 - 120 & 10 120 - 140 & 7 140 - 160 & 9 \end{matrix}$

68.3 hours

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71.1 hours

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75.6 hours

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81.4 hours

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Solution

The correct option is B
71.1 hours

The cumulative frequency table for the
data is given below.

$\begin{matrix} Class & Frequency & Cumulative Interval & Frequency 0 - 20 & 7 & 7 20 - 40 & 13 & 20 40 - 60 & 20 & 40 60 - 80 & 18 & 58 80 - 100 & 16 & 74 100 - 120 & 10 & 84 120 - 140 & 7 & 91 140 - 160 & 9 & 100 \end{matrix}$

$\frac{N}{2} = 50$
Therefore, median class is 60-80
$Median = L + \frac{\frac{N}{2} - c . f}{f} \times h = 60 + \frac{50 - 40}{18} \times 20 = 71.11 h o u r s$

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\begin{matrix} L i f e t i m e (i n h o u r s) & F r e q u e n c y 0 - 20 & 7 20 - 40 & 13 40 - 60 & 20 60 - 80 & 18 80 - 100 & 16 100 - 120 & 10 120 - 140 & 7 140 - 160 & 9 \end{matrix}

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The lifetimes of 100 light bulbs are tabulated below. Find the median lifetime. Lifetime (in hours)Frequency0−20720−401340−602060−801880−10016100−12010120−1407140−1609

The lifetimes of 100 light bulbs are tabulated below. Find the median lifetime.

$\begin{matrix} Lifetime (in hours) & Frequency 0 - 20 & 7 20 - 40 & 13 40 - 60 & 20 60 - 80 & 18 80 - 100 & 16 100 - 120 & 10 120 - 140 & 7 140 - 160 & 9 \end{matrix}$