3 Tutor System
Starting just at 265/hour

# The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table: Length(in mm) Number of leaves 118-126 3 127-135 5 136-144 9 145-153 12 154-162 5 163-171 4 172-180 2 Find the median length of leaves.

Since the data are not continuous reduce 0.5 in the lower limit and add 0.5 in the upper limit.

 Class Interval Frequency Cumulative frequency 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

So, n = 40 and $$\frac{n}{2} \ = \ 20$$

Median class = 144.5 -153.5

then, $$l = 144.5, cf = 17, f = 12, h = 9$$

Now we know that, Median $$= \ l \ + \ ( \frac{ \frac{n}{2} \ - \ cf}{f} ) \ × \ h$$

$$\Rightarrow$$ Median $$= \ 144.5 \ + \ ( \frac{20 \ - \ 17}{12}) \ × \ 9$$

$$= \ 144.5 \ + \ \frac{3}{12} \ × \ 9$$

$$= \ 144.5 \ + \ 2.25 \ = \ 146.75$$

$$\therefore$$ The median length of the leaves = 146.75 mm.