https://file.aiquickdraw.com/mathbot/file/172940756903076vnq2jn.jpg

Let's go through the questions based on the data provided in the image.

The data set consists of the number of animals listed by 23 adults in one minute:
1, 3, 3, 5, 5, 6, 6, 7, 7, 9, 9, 10, 11, 11, 11, 11, 13, 14, 14, 15, 15, 18, 19

**(a) Which measures of central tendency take more than one value?**
- **Mean:** Averages all values. There is only one mean.
- **Median:** The middle value in the ordered list. There is only one median.
- **Mode:** The most frequent value(s). In this case, the mode appears more than once (11 appears four times). 
  **Answer:** **Mode** is the correct answer here because it takes more than one value.

**(b) If the measurement 19 (the largest) were replaced by 40, which measures of central tendency would be affected?**
- **Mean:** Since the mean depends on the total sum of the data, replacing 19 with 40 will increase the mean.
- **Median:** The median depends on the middle value and would remain unchanged because this change affects only one data point.
- **Mode:** The most frequent value(s) won't change.
  **Answer:** **Mean** would be affected.

**(c) If the largest measurement (19) were removed, which measures of central tendency would change?**
- **Mean:** Removing a value will change the total sum and thus the mean.
- **Median:** The median might change since the position of the middle value could shift slightly.
- **Mode:** The mode (most frequent value) would remain unchanged.
  **Answer:** **Mean** and **Median** would change.

**(d) Which best describes the distribution of the original data?**
- **Negatively skewed:** A distribution with a longer left tail (lower values).
- **Positively skewed:** A distribution with a longer right tail (higher values).
- **Roughly symmetrical:** The data is somewhat balanced on both sides of the center.

Since the data has more values towards the lower side but some extreme higher values, the data is **positively skewed**.
  **Answer:** **Positively skewed**.

Let me know if you need further explanation! Here are five related questions to deepen your understanding:

1. How do you calculate the mean for a data set like this one?
2. What would happen to the mode if you added another 19 to the data set?
3. How does skewness affect the mean and median in a distribution?
4. Could the distribution be considered normal if the skewness was removed?
5. What is the difference between a positively skewed and negatively skewed distribution?

**Tip:** When interpreting data distributions, always consider both the graphical shape (like histograms) and numerical summaries (mean, median, mode) for a more complete understanding.

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. The data shows the number of animals listed by 23 non-demented adults. Based on this data, answer the following questions: (a) Which measures of central tendency take more than one value? (b) If the measurement of 19 is replaced by 40, which measures of central tendency are affected? (c) If the largest measurement (19) is removed, which measures of central tendency are affected? (d) What best describes the distribution of the original data?

Analyze the central tendency (mean, median, mode) and the skewness of a data set from a dementia test, where adults are asked to list as many animals as possible. Learn how changes in data affect the measures of central tendency and understand the characteristics of a positively skewed distribution. Suitable for students in Grades 8-10.

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