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 leaves118−126127−135136−144145−153154−162163−171172−18035912542Find the median length of the leaves.

Question

Filo · Accepted Answer

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.)

Converting the given table into exclusive form and preparing the cumulative frequency table, we get

We have,

n = 40

\Rightarrow \frac{n}{2} = 20

The cumulative frequency just greater than

\frac{n}{2}

is

29

and the corresponding class is

144.5 - 153.5

.

Thus,

144.5 - 153.5

is the median class such that

\frac{n}{2} = 20, l = 144.5, c f = 17, f = 12

, and

h = 9

Substituting these values in the formula

Median,

M = l + ⎝ ⎛ \frac{\frac{n}{2} - c f}{f} ⎠ ⎞ \times h

M = 144.5 + (\frac{20 - 17}{12}) \times 9

M = 144.5 + \frac{3}{12} \times 3 = 144.5 + 2.25 = 146.75

Hence, median length

= 146.75

hours

Question Text	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:Find the median length of the leaves.
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

Practice questions from similar books

Length (in mm)	Number of leaves
$118 - 126$ $127 - 135$ $136 - 144$ $145 - 153$ $154 - 162$ $163 - 171$ $172 - 180$	$3$ $5$ $9$ $12$ $5$ $4$ $2$