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.

Step 1: Calculate Class Marks

To find the mean of a grouped frequency distribution, we first need to determine the class mark ($x_i$) 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 $f_i x_i$

Next, we multiply each frequency ($f_i$) by its corresponding class mark ($x_i$). This product, $f_i x_i$, represents the total value contributed by all observations within that class interval.

Step 3: Calculate Sum of Frequencies and Sum of $f_i x_i$

To apply the mean formula, we need the sum of all frequencies ($\Sigma f_i$) and the sum of all $f_i x_i$ values ($\Sigma f_i x_i$). We add up the individual frequencies and the products calculated in the previous step.

Step 4: Calculate the Mean

Finally, we calculate the mean ($\bar{x}$) using the formula for grouped frequency distributions: the sum of $f_i x_i$ divided by the sum of $f_i$.

Step 5: Simplify to find the Mean

Performing the division, we find that the mean of the given frequency distribution is 27.

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