Below given is the frequency distribution of weekly wages of 100 workers in a factory:
Weekly wages (Rs.)
120-124
125-129
130-134
135-139
140-144
145-149
150-154
155-159
160-164
No. of Workers
3
5
12
23
31
10
8
5
3
Calculate the mean median and mode for the given distribution.
Answers
Mean = 135.44
Median = 142
Mode = 135-139 (23 times)
To Find:
to find three measures of central tendency:
Mean: The average weekly wage of the workers
Median: The middle value of the weekly wages (the value that separates the distribution into two equal parts)
Mode: The most frequently occurring weekly wage among the workers.
Given:
A frequency distribution of weekly wages of 100 workers in a factory
The class intervals and corresponding frequencies for the weekly wages of the workers
Solution:
To calculate the mean, median and mode for the given frequency distribution:
Mean:
To calculate the mean, we first need to find the midpoint of each class interval and then multiply it by the corresponding frequency.
Next, we add up all of these products and divide by the total number of observations (100 in this case).
(1223 + 1275 + 13212 + 13723 + 14231 + 14710 + 1528 + 1575 + 162*3)/100 = 135.44
Median:
To find the median, we need to find the value that separates the distribution into two equal parts, i.e. half of the observations lie below it and half lie above it.
Here, we know that the cumulative frequency at the median class is (100/2) = 50.
So, we need to find the class interval that corresponds to the cumulative frequency of 50.
In this case it is the 5th class interval, with a range of 140-144. The median is 142.
Mode:
The mode is the value that appears most frequently in the distribution.
In this case, it is the 4th class interval (135-139) with a frequency of 23.
Therefore,Mean = 135.44
Median = 142
Mode = 135-139 (23 times)
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