Find the median length of leaves.

solution:

Since the information are not ceaseless diminish 0.5 in as far as possible and add 0.5 in as far as possible.

Class Interval      Frequency           Cumulative recurrence

117.5-126.5        3             3

126.5-135.5        5             8

135.5-144.5        9             17

144.5-153.5        12           29

153.5-162.5        5             34

162.5-171.5        4             38

171.5-180.5        2             40

In this way, the information got are:

\[n\text{ }=\text{ }40\text{ }and\text{ }n/2\text{ }=\text{ }20\]

\[Middle\text{ }class\text{ }=\text{ }144.5-153.5\]

then, at that point, l = 144.5,

cf = 17, f = 12 and h = 9

\[Middle\text{ }=\text{ }144.5+\left( \left( 20-17 \right)/12 \right)\times 9\]

\[=\text{ }144.5+\left( 9/4 \right)\]

\[=\text{ }146.75\text{ }mm\]

Subsequently, the middle length of the leaves = 146.75 mm.