The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table: Length (in mm) Number of leaves 118-126 1 127-135 1 136-144 1 145-153 1 154-162 1 163-171 1 172-180 3 59 12 5 4 2 Find the median length of the leaves.

The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to(117.5−1;26.5,126.5−1;35.5,...,171.5−1;80.5)Converting the given table into exclusive form and preparing the cumulative frequency table, we getWe have,n=40⇒n2=20The cumulative frequency just greater thann2is29and the corresponding class is144.5−1;53.5.Thus,144.5−1;53.5is the median class such thatn2=20,l=144.5,cf=17,f=12, andh=9Substituting these values in the formulaMedian,M=l+⎛⎜⎜⎝n2−cff⎞⎟⎟⎠×hM=144.5+(20−1;712)×9M=144.5+312×3=144.5+2.25=146.75Hence, median length=146.75hours