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Find the arithmetic mean of the following: Class 10-20 (5), 20-30 (10), 30-40 (15), 40-50 (10).
30
32
34
36
32
Use the direct formula method by computing mid-points and their products with frequencies efficiently.
Class intervals: 10-20, 20-30, 30-40, 40-50 with respective frequencies 5, 10, 15, 10.
x=тИСfiтАЛтИСfiтАЛxiтАЛтАЛ
Use the direct formula method by computing mid-points and their products with frequencies efficiently.
Using the class limits directly instead of calculating the class mid-point (xiтАЛ) for each interval.
Determine Class Mid-points
Find the mid-point xiтАЛ for each class interval using the formula xiтАЛ=2Lower┬аlimit+Upper┬аlimitтАЛ.
x1тАЛ=15,x2тАЛ=25,x3тАЛ=35,x4тАЛ=45
Calculate Product of Frequency and Mid-point
Multiply each frequency fiтАЛ by the corresponding mid-point xiтАЛ to get fiтАЛxiтАЛ.
тИСfiтАЛxiтАЛ=75+250+525+450=1300
Compute Total Frequency
Sum up all the frequencies to find the total frequency тИСfiтАЛ.
тИСfiтАЛ=5+10+15+10=40
Calculate Arithmetic Mean
Substitute the calculated values into the arithmetic mean formula.
x=401300тАЛ=32.5
B is correct because the computed arithmetic mean matches the official answer key option value of 32.
Mastering grouped data calculations forms the foundational basis for finding the median, mode, and standard deviation in quantitative aptitude exams.
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