Find median and mode from the following distribution
Daily wages 200-400 400-600 600-800 800-1000 1000-1200 1200-1400
No of workers 6 9 15 10 7 3
Answers
Step-by-step explanation:
here is the answer
left side is the answer for median and
right side is the answer for mode.
hope it may help you.
Concept:
The median of grouped data is calculated by,
Median = l + [ { (n/2) - cf } /f]× h
where l is the lower class limit of the median class, h is Class size, f is the frequency of the median class, n is the total frequency and cf is the Cumulative frequency of the class which is preceding the median class.
The mode of grouped data can be calculated by,
Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)]×h
Where l is the lower class limit of modal class, h is class size, f₁ is the frequency of modal class, f₀ is the frequency of class proceeding to modal class, and f₂ is the frequency of class succeeding to modal class.
Given:
A table of frequency distribution is given.
Find:
The median and mode of the given frequency distribution.
Solution:
The frequency distribution table is attached,
Median = l + [ { (n/2) - cf } /f]× h
Now, substituting the given values, median class is 600-800
Median = 600 + [ { (50/2) - 15} /15]× 200
Median = 600 + [ 10/15] × 200
Median = 600 + 133.33
Median = 733.33
Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)]×h
Now, substituting the values, the modal class is 600-800,
Mode = 600 + [( 15 - 9 )/(2×15 - 9 - 10 )]× 200
Mode = 600 + [( 6 )/(11 )]× 200
Mode = 600 + 109.09
Mode = 709.09
Hence, the median and mode of the frequency distribution are 733.33 and 709.09 respectively.
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