The following table gives the distribution of the life time of 400 neon lamps:
Find the median lifetime of a lamp.
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
From the table, it can be observed that n = 400 ⇒ n/2 = 200
Cumulative frequency (cf) just greater than 200 is 216, belonging to class 3000 - 3500.
Therefore, median class = 3000 - 3500
Class size, h = 500
Lower limit of median class, l = 3000
Frequency of median class, f = 86
Cumulative frequency of class preceding median class, cf = 130
Median = l + [(n/2 - cf)/f] × h
= 3000 + [(200 - 130)/86] × 500
= 3000 + (70 × 500)/86
= 3000 + 17500/43
= 3000 + 406.98
= 3406.98
Therefore, median lifetime of lamps is 3406.98 hours.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 14
Video Solution:
The following table gives the distribution of the life time of 400 neon lamps: Find the median lifetime of a lamp.
NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.3 Question 5
Summary:
The median lifetime of a lamp, given the distribution of the lifetime of 400 neon lamps is 3406.98 hours.
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