Monthly pocket money of students of a class is given in the following frequency distribution:
13
175 - 200
200 - 225
Pocket Money 100 - 125 125 - 150 150 - 175
ſin QAR]
Frequency
14
8
12
Find the mean pocket money of the students in the class.
5
11
Answers
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Answer:
Mean pocket money = 23,750/47 = 506.38
Step-by-step explanation:
From the above question,
They have given :
To find the mean (average) pocket money of the students in the class, we need to calculate the weighted average.
We start by finding the midpoint of each pocket money range and multiplying it by the corresponding frequency. Then we sum these products and divide by the total frequency (number of students).
The midpoint of the pocket money range,
100-125 is (100 + 125)/2 = 112.5
The midpoint of the pocket money range,
125-150 is (125 + 150)/2 = 137.5
The midpoint of the pocket money range,
150-175 is (150 + 175)/2 = 162.5
The midpoint of the pocket money range,
175-200 is (175 + 200)/2 = 187.5
The midpoint of the pocket money range 200-225 is
(200 + 225)/2 = 212.5
The product of midpoint and frequency for the pocket money range,
100-125 is 112.5 * 14 = 1575
The product of midpoint and frequency for the pocket money range,
125-150 is 137.5 * 8 = 1100
The product of midpoint and frequency for the pocket money range,
150-175 is 162.5 * 12 = 1958
The sum of these products is 1575 + 1100 + 1958 = 4533
The mean pocket money is the sum of these products divided by the total frequency (number of students),
which is 4533 / 34 = 133.68 QAR.
For the range of 175-200, the midpoint is calculated as,
(175 + 200)/2 = 187.
The total amount of pocket money can thus be calculated as:
(14 x 112.5) + (8 x 137.5) + (12 x 162.5) + (13 x 187.5) = 23,750
The mean pocket money of the students can be calculated by dividing the total amount of pocket money by the total number of students.
Mean pocket money = 23,750/47 = 506.38
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