UPTET Paper 1 Model Test 2

Concept:The median for grouped data is the value that divides the distribution into two equal halves. The formula uses the lower limit of the median class, cumulative frequency before it, frequency, and class width.Explanation:Step 1: Identify the given values.$L = 40$ (lower boundary of median class)$N = 120$ (total frequency)$F = 35$ (frequency of median class)$C = 37$ (cumulative frequency of the class just before the median class)$H = 20$ (class width)Step 2: Find $\frac{N}{2} = \frac{120}{2} = 60$.Step 3: Apply the median formula: $$Median = L + \frac{\frac{N}{2} - C}{F} \times H$$Substitute the values: $$Median = 40 + \frac{60 - 37}{35} \times 20$$Step 4: Calculate inside the fraction: $60 - 37 = 23$.Then $\frac{23}{35} \times 20 = \frac{460}{35} \approx 13.1429$.Step 5: Add to $L$: $40 + 13.1429 = 53.1429 \approx 53.14$.Answer:$Median = 53.14$ (Option D)