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Let's break down the questions step by step based on the data provided:

### Given Data:
The ages at which 22 retirees retired are:
31, 43, 47, 47, 51, 52, 56, 58, 61, 61, 66, 67, 67, 67, 68, 68, 69, 72, 72, 74, 74, 77

### (a) Measures of central tendency that take more than one value:
- **Mean**: The mean (average) is a single value calculated by summing all data points and dividing by the number of data points. The mean takes only one value.
- **Median**: The median is the middle value when data points are ordered. It takes only one value in most cases.
- **Mode**: The mode is the most frequent value(s) in a dataset. Here, we have three modes: 67, 68, and 72 (each appears more than once).

Thus, **Mode** is the measure that takes more than one value.

### (b) Impact of replacing 31 with 24 on measures of central tendency:
- **Mean**: Yes, the mean would be affected since replacing a value changes the total sum, which alters the mean.
- **Median**: No, replacing 31 with 24 would not affect the median because the order of the middle values in the data would stay the same.
- **Mode**: No, the mode is not affected as 31 is not one of the modes. Replacing it does not change the frequency of the modal values.

Thus, **Mean** would be affected.

### (c) Impact of removing the smallest measurement (31):
- **Mean**: Yes, removing a value affects the total sum, which changes the mean.
- **Median**: No, since the median focuses on the middle value, removing the smallest measurement does not impact it.
- **Mode**: No, the mode would not change as 31 is not a mode, and removing it does not change the frequencies of the modal values.

Thus, **Mean** would be affected.

### Summary of Answers:
- (a) Mode
- (b) Mean
- (c) Mean

Would you like more details on any part of this explanation or further clarifications?

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Here are five related questions to deepen your understanding:
1. How is the mean affected by the addition of extreme values in a dataset?
2. What happens to the median when an outlier is introduced?
3. How is the mode useful in interpreting a dataset with multiple peaks?
4. If more data points were added near the highest age (77), how would that impact the mean, median, and mode?
5. What is the impact of having more than one mode on interpreting a dataset?

**Tip:** The mode is especially useful in datasets where some values repeat frequently, and it can provide insights into common trends.

A survey of 22 retirees was taken, and their ages at retirement were collected. The problem involves determining which central tendency measures (mean, median, mode) take more than one value and identifying how certain changes to the data (such as replacing or removing the smallest value) affect these measures.

This problem involves analyzing the central tendency measures (mean, median, mode) of the ages at which 22 retirees retired. Learn how changing or removing data points affects these measures. Suitable for Grades 8-10.

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