Mathematics

Mathematics

Problem

Find the missing frequency 'f' in the following table, if the mean of the given data is 18. Hence find the mode.
Daily AllowanceNumber of Children
11 – 137
13 – 156
15 – 179
17 – 1913
19 – 21f
21 – 235
23 – 254
Intuitive explanation

The mean of grouped data depends on the sum of all frequencies and the weighted sum of class midpoints. Since you know the mean is 18, you can set up an equation using the formula Mean=∑f⋅x∑f\text{Mean} = \frac{\sum f \cdot x}{\sum f}, where xx is each class midpoint and ff is frequency. Solve for the unknown frequency, then identify the mode as the class with the highest frequency.

Intuitive explanation

The mean of grouped data depends on the sum of all frequencies and the weighted sum of class midpoints. Since you know the mean is 18, you can set up an equation using the formula Mean=∑f⋅x∑f\text{Mean} = \frac{\sum f \cdot x}{\sum f}, where xx is each class midpoint and ff is frequency. Solve for the unknown frequency, then identify the mode as the class with the highest frequency.

Browse the problem library