Question 13 of 15intermediate🔍 AnalyzeShort Answer3 marks

The weights of people in a group were measured every month. The average weight for the previous month was 65.3 kg and the median weight was 67 kg. The data for this month showed that one person has lost 2 kg and two have gained 1 kg. What can we say about the change in mean weight and median weight this month?

Correct Answer

For the mean: Net change in total weight = (-2) + 1 + 1 = 0 kg Since the total weight hasn't changed, the mean remains the same at 65.3 kg.

For the median: Without knowing the positions of these three people in the sorted weight distribution, we cannot determine how the median changes.

Exercise: Figure it Out (Section 3) | Q: 8 | (Page Page 27)
For More Understanding

Explanation

The chapter explains that the mean depends on the total sum of values. If the net change in total is zero, the mean stays the same. The median depends on the middle position in sorted data, which may or may not change depending on where the weight changes occurred.

Solution Steps

  1. Step 1: Calculate net change in total weight: -2 + 1 + 1 = 0 kg

  2. Step 2: Since total weight is unchanged, mean = 65.3 kg (unchanged)

  3. Step 3: For median, we need to know if the weight changes affect the middle positions

  4. Step 4: Without knowing positions of these people in the sorted distribution, median change cannot be determined

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