Question

2. Q. The length of the 40 leaves of plants given below
Length in mm
118-126
127-135
136-144
145-153
154-162
No. of leaves 12
7
5
14
2
One leaves picked up randomly, find the probability that the leaf picked was of length
(a)more than 126 mm and less than 136 mm (b)more than 126 mm (c)less than 154 mm
​

Answer 1

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

⇒

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