Question:
Find the median income per day ifIncome (₹) per day 1000 1500 800 2000 1800 2500 No. of persons 24 21 16 20 11 30
Find the median income per day if
| Income (₹) per day | 1000 | 1500 | 800 | 2000 | 1800 | 2500 |
| No. of persons | 24 | 21 | 16 | 20 | 11 | 30 |
Updated On: Sep 16, 2026
- ₹ 1500
- ₹ 1400
- ₹ 800
- ₹ 1650
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The Correct Option is D
Solution and Explanation
Concept:
Step 1: Arrange incomes in ascending order with their frequencies and find total N
₹800(16), ₹1000(24), ₹1500(21), ₹1800(11), ₹2000(20), ₹2500(30)
N = 16 + 24 + 21 + 11 + 20 + 30 = 122
Step 2: Build the cumulative frequency table
₹800 → c.f. 16
₹1000 → c.f. 40
₹1500 → c.f. 61
₹1800 → c.f. 72
₹2000 → c.f. 92
₹2500 → c.f. 122
Step 3: Find the required positions since N = 122 is even
Median = average of the 61st and 62nd values (N/2 = 61 and N/2 + 1 = 62)
Step 4: Locate the 61st and 62nd values using the c.f. column
c.f. reaches exactly 61 at income ₹1500, so the 61st value = ₹1500
The 62nd value falls at income ₹1800 (c.f. goes from 61 to 72 there)
Step 5: Calculate the median
Median = (1500 + 1800)/2 = 3300/2 = ₹1650
Final Answer: ₹1650
- For an ungrouped frequency distribution, arrange the values in ascending order and build the cumulative frequency (c.f.) table.
- When total frequency N is even, median = average of the (N/2)th and (N/2 + 1)th observations.
- Locate these two positions using the c.f. column.
Step 1: Arrange incomes in ascending order with their frequencies and find total N
₹800(16), ₹1000(24), ₹1500(21), ₹1800(11), ₹2000(20), ₹2500(30)
N = 16 + 24 + 21 + 11 + 20 + 30 = 122
Step 2: Build the cumulative frequency table
₹800 → c.f. 16
₹1000 → c.f. 40
₹1500 → c.f. 61
₹1800 → c.f. 72
₹2000 → c.f. 92
₹2500 → c.f. 122
Step 3: Find the required positions since N = 122 is even
Median = average of the 61st and 62nd values (N/2 = 61 and N/2 + 1 = 62)
Step 4: Locate the 61st and 62nd values using the c.f. column
c.f. reaches exactly 61 at income ₹1500, so the 61st value = ₹1500
The 62nd value falls at income ₹1800 (c.f. goes from 61 to 72 there)
Step 5: Calculate the median
Median = (1500 + 1800)/2 = 3300/2 = ₹1650
Final Answer: ₹1650
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