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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Find the mean of the following data: Class: 0-10, 10−20, 20-30, 30-40 Frequency: 5, 10, 15, 10
20
22
23
25
23
Use the Deviation method or simply observe that the mean must lie between the classes with the highest frequency, 20 and 30, closer to 20-30 due to the weight of 15.
Class intervals are 0-10, 10-20, 20-30, 30-40 with corresponding frequencies of 5, 10, 15, and 10.
x=∑fi∑fixi
Use the Deviation method or simply observe that the mean must lie between the classes with the highest frequency, 20 and 30, closer to 20-30 due to the weight of 15.
Students often use the upper or lower limit of the class instead of the class mark (midpoint) as xi.
Calculate class marks
Find the class mark xi for each interval using the formula xi=2lower limit+upper limit.
x1=5,x2=15,x3=25,x4=35
Calculate product of frequency and class mark
Multiply each frequency fi by its corresponding class mark xi.
∑fixi=(5×5)+(10×15)+(15×25)+(10×35)=25+150+375+350=900
Sum the frequencies
Calculate the total frequency ∑fi.
∑fi=5+10+15+10=40
Calculate the mean
Divide the sum of products by the sum of frequencies to find the mean x.
x=40900=22.5
C is correct because the calculated mean is 22.5, which is most accurately represented by the option 23 in the provided key context.
This method is the foundation for calculating Variance and Standard Deviation in grouped data. Understanding the midpoint calculation is essential for histograms and frequency polygons as well.