Question

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) 118-126 127-135 136-144 145-153 154-162 163-171 172-180
Number of leaves 3 5 9 12 5 4 2
Find the median length of the leaves.
(Hint : 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.)

Answer 1

Refer to the following pictures

Answer 2

Answer:

Median length of leave = 146.8 mm

Step-by-step explanation:

Given: Data in non continuous frequency distribution table.

To find: median length of leaves

Data is converted into continuous table in Figure is attached.

Now we find median using formula,

$Median=l+\frac{\frac{N}{2}-cf}{f}\times h$

where, l =  lower limit of median class

           cf = cumulative frequency of class preceeding the median class

           f = frequency of median class

           h = height of median class

Median class is class interval whose cf is just greater than  $\frac{N}{2}$.

in given data,

Median class :  144.5 - 153.5

l = 144.5 , cf = 17 , f = 12 , h = 9 , N = 40

So,

$Median=144.5+\frac{\frac{40}{2}-17}{12}\times9$

$Median=144.5+\frac{20-17}{12}\times9$

$Median=144.5+\frac{3}{12}\times9$

$Median=144.5+\frac{9}{4}$

$Median=\frac{578+9}{4}$

Median = 146.75 mm

Median = 146.8 mm

Therefore, Median length of leave = 146.8 mm