Question

4. 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
127-135
136-144
145-153
12
154 - 162
3
163-171
171
-180
Find the mean length of the leaves.​

Answer 1

Answer:

Ur answer

Step-by-step explanation:

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

⇒

2

n

=20

The cumulative frequency just greater than

2

n

is 29 and the corresponding class is 144.5−153.5.

Thus, 144.5−153.5 is the median class such that

2

n

=20,l=144.5,cf=17,f=12, and h=9

Substituting these values in the formula

Median, M=l+

⎝

⎛

f

2

n

−cf

⎠

⎞

×h

M=144.5+(

12

20−17

)×9

M=144.5+

12

3

×3=144.5+2.25=146.75

Hence, median length =146.75 hours

solution