Let's go through the questions in the image one by one:

1. Part (a): The question asks for the appropriate measures of center and variability to use with the data, and to explain the reasoning.

   • The measure of center can be the mean (average) or median (middle value). Since heart rate data often follows a distribution where outliers (very high or very low values) can affect the mean, using the median would be a more appropriate measure of center here to avoid the influence of outliers.
   • The measure of variability should be something that considers how spread out the data points are. A common choice is the range (difference between the highest and lowest values) or the interquartile range (IQR), which measures the spread of the middle 50% of data. Given the dot plots, it might also be useful to consider standard deviation to capture how each point deviates from the center.

   Reasoning: Median is preferred for the center if there are outliers, and standard deviation or IQR is suitable for variability to capture the spread of the data.

2. Part (b): Which situation shows a higher typical heart rate?

   • You have already selected B, which appears correct. From the dot plots, Situation B has more data points clustered at higher heart rates compared to Situation A.

3. Part (c): Which situation shows greater variability?

   • You selected Situation B. By observing the dot plot, Situation B shows a more spread-out distribution (points are more scattered across the range), indicating greater variability compared to Situation A, where the points are more concentrated.

Would you like more details or have any questions?

Here are 5 questions that expand on this:

1. What is the difference between the standard deviation and interquartile range as measures of variability?
2. Why might the mean be less reliable than the median for skewed data?
3. How can outliers influence measures of center and variability in datasets?
4. What other statistical tools could you use to analyze heart rate data besides mean, median, and standard deviation?
5. How would you visually represent the variability in the heart rate data to make it more understandable?

Tip: Always check for outliers when calculating mean or standard deviation, as they can greatly influence the results!