UPSC CDS 2 2022 Math Paper

Concept:The mean of a frequency distribution is calculated using the formula $\bar{x} = \frac{\sum f x}{\sum f}$. Here, the total frequency and mean are known, so we can find the missing frequency $q$.Explanation:Given: total frequency $N = 200$ and mean $= 1.46$.The frequency distribution table is:Step 1: Use total frequency to find $p + q$.$46 + p + q + 25 + 10 + 5 = 200$$\Rightarrow p + q + 86 = 200$$\Rightarrow p + q = 114$ ----- (1)Step 2: Use the mean formula.Mean $= \frac{\sum f x}{N} = \frac{p + 2q + 140}{200} = 1.46$$\Rightarrow p + 2q + 140 = 292$$\Rightarrow p + 2q = 152$ ----- (2)Step 3: Subtract equation (1) from equation (2).$(p + 2q) - (p + q) = 152 - 114$$\Rightarrow q = 38$Thus, the missing frequency $q$ is $38$.Answer:$q = 38$