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.
(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.).
Solution:
We know that,
Median = l + [(n/2 - cf)/f] × h
- Class size, h
- Number of observations, n
- Lower limit of median class, l
- Frequency of median class, f
- Cumulative frequency of class preceding median class, cf
Let's construct a continuous class data.
From the table, it can be observed that n = 40 ⇒ n/2 = 20
Cumulative frequency (cf) just greater than 20 is 29, belonging to class 144.5 - 153.5
Therefore, median class = 144.5 - 153.5
Class size, h = 9
Lower limit of median class, l = 144.5
Frequency of median class, f = 12
Cumulative frequency of class preceding median class, cf = 17
Median = l + [(n/2 - cf)/f] × h
= 144.5 + [(20 - 17)/12] × 9
= 144.5 + (3/12) × 9
= 144.5 + 9/4
= 144.5 +2.25
= 146.75
Therefore, median length of leaves is 146.75 mm.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 14
Video Solution:
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.
NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.3 Question 4
Summary:
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: The median length of the leaves for a plant having 40 leaves is 146.75 mm.
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