The following table gives the distribution of the lifetime of 200 wristwatches.
Life Time (In hours) | 1000-1500 | 1500-2000 | 2000-2500 | 2500-3000 | 3000-3500 | 3500-4000 | 4000-4500 |
Number of wristwatches |
12 | 24 | 56 | 34 | 45 | 56 | 65 |
What will be the median lifetime of a wristwatch?
3408.82 hours
3222.22 hours
3444.22 hours
4408.82 hours
option (B)3222.22
The following table gives the distribution of the lifetime of 200 wristwatches.
Life Time (In hours) | 1000-1500 | 1500-2000 | 2000-2500 | 2500-3000 | 3000-3500 | 3500-4000 | 4000-4500 |
Number of wristwatches |
12 | 24 | 56 | 34 | 45 | 56 | 65 |
From the given table, we have the frequency distribution table as,
Life Time (In hours) | 1000-1500 | 1500-2000 | 2000-2500 | 2500-3000 | 3000-3500 | 3500-4000 | 4000-4500 |
Number of wristwatches |
12 | 24 | 56 | 34 | 45 | 56 | 65 |
Cumulative frequency | 12 | 36 | 92 | 126 | 171 | 227 | 292 |
We have,
Here, the cumulative frequency just greater than 146 is 171 and the corresponding class is 3000-3500.
Therefore, the median class is 3000-3500.
We know the general formula for median of grouped data is,
Where,
=lower limit of the median class,
=size of the median class,
= frequency of the median class,
= sum of frequencies and
=cumulative frequency of the class just preceding the median class.
We have,
Calculating the median, we get,
Therefore, the median lifetime of a wristwatch = 3222.22 hours.
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