Question

find the mean and median of the data
class 118-126 126-134 134-142 142-150 150-158 158-166
fi 4,5 ,10,12,4,5​

Answer 1

$ANSWER</p><p></p><p></p><p>The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to (117.5−126.5,126.5−135.5,...,171.5−180.5.)</p><p></p><p>Converting the given table into exclusive form and preparing the cumulative frequency table, we get</p><p></p><p></p><p>We have, n=40</p><p></p><p>⇒2n=20</p><p></p><p></p><p>The cumulative frequency just greater than 2n is 29 and the corresponding class is 144.5−153.5.</p><p></p><p></p><p>Thus, 144.5−153.5 is the median class such that</p><p></p><p>2n=20,l=144.5,cf=17,f=12, and h=9</p><p></p><p></p><p>Substituting these values in the formula</p><p></p><p>Median, M=l+⎝⎛f2n−cf⎠⎞×h</p><p></p><p></p><p>M=144.5+(1220−17)×9</p><p></p><p></p><p>M=144.5+123×3=144.5+2.25=146.75</p><p></p><p>       </p><p>Hence, median length =146.75 hours</p><p></p><p></p><p></p><p>$

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