Find the mean of the following frequency distribution: class intervals 0-10, 10-20, 20-30, 30-40, 40-50 with frequencies 5, 8, 15, 16, 6.
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Step-by-Step Solution
Step 1: Calculate Class Marks
To find the mean of a grouped frequency distribution, we first need to determine the class mark (xi) for each class interval. The class mark is the midpoint of the class interval, calculated by adding the upper and lower limits of the class and dividing by 2.
Step 2: Calculate fixi
Next, we multiply each frequency (fi) by its corresponding class mark (xi). This product, fixi, represents the total value contributed by all observations within that class interval.
Step 3: Calculate Sum of Frequencies and Sum of fixi
To apply the mean formula, we need the sum of all frequencies (Σfi) and the sum of all fixi values (Σfixi). We add up the individual frequencies and the products calculated in the previous step.
Step 4: Calculate the Mean
Finally, we calculate the mean (xˉ) using the formula for grouped frequency distributions: the sum of fixi divided by the sum of fi.
Step 5: Simplify to find the Mean
Performing the division, we find that the mean of the given frequency distribution is 27.