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Find the mean of the following frequency distribution: Marks (10, 20, 30, 40) with frequencies (5, 8, 12, 5).
26.25
25.75
27.50
24.80
26.25
Use a tabular approach to quickly compute products fiтАЛxiтАЛ row by row, then sum them up and divide by total frequency to save time in the exam hall.
Marks (xiтАЛ): 10, 20, 30, 40 and corresponding frequencies (fiтАЛ): 5, 8, 12, 5
x=тИСfiтАЛтИСfiтАЛxiтАЛтАЛ
Use a tabular approach to quickly compute products fiтАЛxiтАЛ row by row, then sum them up and divide by total frequency to save time in the exam hall.
Multiplying frequencies directly with each other or forgetting to divide by the total sum of frequencies тИСfiтАЛ.
Calculate products of marks and frequencies
Multiply each mark xiтАЛ by its corresponding frequency fiтАЛ: 10imes5=50, 20imes8=160, 30imes12=360, and 40imes5=200.
тИСfiтАЛxiтАЛ=50+160+360+200=770
Find the total frequency
Add all the individual frequencies together to find the total number of observations.
тИСfiтАЛ=5+8+12+5=30
Apply the mean formula for grouped data
Substitute the values of тИСfiтАЛxiтАЛ and тИСfiтАЛ into the arithmetic mean formula.
x=30770тАЛ=377тАЛ=26.25
A is correct because the calculated mean of the frequency distribution is 26.25.
Understanding grouped data statistics is essential for handling continuous frequency distributions using assumed mean or step-deviation methods in later exam questions.
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