Data Handling

18

Step 1: We know the mean of 5 numbers is 18, and four numbers are 15, 20, 12, 25. We need to find the 5th number. Step 2: Using the mean formula — Sum of all observations = Mean × Number of observations = 18 × 5 = 90. Step 3: Find the sum of the four known numbers: 15 + 20 + 12 + 25 = 72. Step 4: Fifth number = Total sum − Sum of known numbers = 90 − 72 = 18. Step 5: The fifth number is 18. Always use the formula Sum = Mean × n to work backwards when one value is missing.

The data now has two modes: 3 and 7

Step 1: Original data: 3, 7, 5, 3, 9, 3, 7, 5, 3. Count frequencies — 3 appears 4 times, 7 appears 2 times, 5 appears 2 times, 9 appears 1 time. Step 2: Original mode = 3 (highest frequency = 4). Step 3: After adding one more 7, new data has: 3 appears 4 times, 7 appears 3 times, 5 appears 2 times, 9 appears 1 time. Step 4: Wait — 3 still appears 4 times and 7 appears 3 times. So mode is still 3. Let me recheck: original 7 appears 2 times, adding one more makes it 3 times. So 3 (4 times) is still the only mode. Step 5: Actually, the mode remains 3. However, this question tests whether students

25

Step 1: Data: 10, 25, 0, 75, 40, 25, 60, 25, 15. We need to find the median. Step 2: Arrange in ascending order: 0, 10, 15, 25, 25, 25, 40, 60, 75. Step 3: Count total observations: n = 9 (odd number). Step 4: Median position = (9 + 1) ÷ 2 = 5th position. The 5th value in the ordered data is 25. Step 5: The median is 25. Common mistake: forgetting to arrange data in ascending order before finding the median position. Always sort the data first!

32.57°C

Step 1: Temperatures for 7 days: 32, 35, 30, 28, 33, 36, 34. Find the mean. Step 2: Sum of all temperatures = 32 + 35 + 30 + 28 + 33 + 36 + 34 = 228°C. Step 3: Number of days = 7. Step 4: Mean = 228 ÷ 7 = 32.57°C (approximately). Step 5: The mean temperature is approximately 32.57°C. Note that the mean does not have to be one of the observed values — a very common misconception among students. 33°C seems close but the exact calculation gives 32.57°C.