Question 6 of 7intermediate🔧 ApplyNumerical4 marks

The size of land holdings of 380 families in a village is given below. Find the median size of land holdings. Size of Land Holdings (in acres) Less than 100 100–200 200 – 300 300–400 400 and above. Number of families 40 89 148 64 39

Correct Answer

The median size of land holdings is 241.22 acres.

Exercise: EXERCISES | Q: 7 | (Page 15)
For More Understanding

Explanation

This question requires calculating median for a continuous frequency distribution. The median is the value that divides the distribution into two equal parts. For grouped data, we first find the cumulative frequencies, locate the median class using N/2, and then apply the median formula. The answer matches the textbook answer of 241.22 acres.

Solution Steps

  1. Step 1: Calculate cumulative frequency (cf). For classes Less than 100, 100-200, 200-300, 300-400, 400 and above, the cf values are 40, 129, 277, 341, and 380 respectively.

  2. Step 2: Find N/2. N = 380, so N/2 = 380/2 = 190.

  3. Step 3: Identify median class. The cumulative frequency just greater than 190 is 277, which lies in the class 200-300. Hence, median class is 200-300.

  4. Step 4: Apply median formula: Median = L + [(N/2 - cf)/f] × h, where L = 200 (lower limit), cf = 129 (cumulative frequency before median class), f = 148 (frequency of median class), h = 100 (class width).

  5. Step 5: Calculate: Median = 200 + [(190 - 129)/148] × 100 = 200 + (61/148) × 100 = 200 + 41.22 = 241.22 acres.

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