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Find the arithmetic mean of the following data (correct to two places of decimals). Class- 5-15 15-25 25-35 35-45 45-55 55-65 interval Frequency 12 18 8 14 16 8
33.68
43.72
22.38
39.45
33.68
Calculate the mid-points (xiтАЛ) first: 10, 20, 30, 40, 50, 60. Use the Assumed Mean Method if the numbers are large, but here, standard multiplication is quick: (120+360+240+560+800+480) / (12+18+8+14+16+8).
Class intervals: 5-15, 15-25, 25-35, 35-45, 45-55, 55-65. Frequencies: 12, 18, 8, 14, 16, 8.
x=тИСfiтАЛтИСfiтАЛxiтАЛтАЛ
Calculate the mid-points (xiтАЛ) first: 10, 20, 30, 40, 50, 60. Use the Assumed Mean Method if the numbers are large, but here, standard multiplication is quick: (120+360+240+560+800+480) / (12+18+8+14+16+8).
Many students use the class interval range instead of the class mid-point (xiтАЛ) or calculate the sum of frequencies (N) incorrectly.
Calculate Mid-points (xiтАЛ)
The mid-point is calculated as (lower limit + upper limit) / 2 for each interval.
xiтАЛ={10,20,30,40,50,60}
Calculate Product of fiтАЛ and xiтАЛ
Multiply each frequency by its corresponding mid-point: 1210=120, 1820=360, 830=240, 1440=560, 1650=800, 860=480.
тИСfiтАЛxiтАЛ=120+360+240+560+800+480=2560
Calculate Total Frequency (N)
Sum the frequencies given in the data.
тИСfiтАЛ=12+18+8+14+16+8=76
Apply Arithmetic Mean Formula
Divide the total sum by the total frequency to find the mean.
x=762560тАЛтЙИ33.6842
A is correct because the calculated arithmetic mean x=2560/76тЙИ33.68.
This concept is foundational for Statistics (Variance/Standard Deviation) and Probability distributions in competitive exams.
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