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### Data Summary:
The numbers listed represent the number of animals a sample of 23 non-demented adults could list in one minute. Here are the data points:  
**1, 3, 3, 5, 5, 6, 7, 7, 9, 9, 10, 11, 11, 11, 11, 13, 14, 14, 15, 15, 18, 19**

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#### (a) For these data, which measures of central tendency take more than one value? (Choose all that apply)
- **Mode** takes more than one value. The value "11" appears four times, making it the mode of the dataset. So it can be selected. There’s only one mode here, but no other measures take multiple values.
  
  Answer: **Mode**

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#### (b) Suppose that the measurement 19 (the largest measurement in the data set) were replaced by 40. Which measures of central tendency would be affected by the change? (Choose all that apply)
- **Mean**: Yes, the mean would increase since 19 is replaced by 40, which is much larger.
- **Median**: No, the middle values remain the same.
- **Mode**: No, this change doesn't affect the frequency of any particular number.

  Answer: **Mean**

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#### (c) Suppose that, starting with the original data set, the largest measurement were removed. Which measures of central tendency would be changed from those of the original data set? (Choose all that apply)
- **Mean**: Yes, removing the largest number (19) would decrease the mean.
- **Median**: No, the middle value of the dataset remains unchanged.
- **Mode**: No, removing 19 does not affect the mode.

  Answer: **Mean**

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#### (d) Which of the following best describes the distribution of the original data? (Choose only one)
- The distribution appears to be **roughly symmetrical**, as the histogram shows a relatively balanced shape around the middle values (with no clear skew).

  Answer: **Roughly symmetrical**

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### Would you like to go into further detail on any of the questions? Here are 5 questions that expand on the information:

1. How is the mean calculated for the given data?
2. What is the importance of the mode in this dataset?
3. How does removing an outlier typically affect the mean and median?
4. What are the characteristics of positively and negatively skewed distributions?
5. How would the central tendencies change if the largest and smallest values were both removed?

**Tip:** Central tendency measures like mean, median, and mode can give different insights into the data, especially when the data is skewed or contains outliers.

Adults who are being tested for dementia are asked to perform mental tasks such as listing as many animals as they can in one minute. Here are the numbers of animals listed in one minute by 23 normal (non-demented) adults: 1, 3, 3, 5, 5, 6, 7, 7, 9, 9, 10, 11, 11, 11, 11, 13, 14, 14, 15, 15, 18, 19. For these data, which measures of central tendency take more than one value? Suppose that the measurement 19 (the largest measurement in the data set) were replaced by 40. Which measures of central tendency would be affected by the change? Suppose that, starting with the original data set, the largest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Which of the following best describes the distribution of the original data?

Explore the analysis of central tendency measures like mean, median, and mode in a dataset from a dementia test. Understand how data changes affect these measures and interpret the data distribution as symmetrical, positively skewed, or negatively skewed. Suitable for students in Grades 10-12.

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