Question

practice problems
1 twenty students participated in a psychology experiment that measured their heart rates in two different situations.
situation a
situation b
a. what are the appropriate measures of center and variability to use with the data?
explain your reasoning.
b. which situation shows a greater typical heart rate?
c. which situation shows greater variability?
2 a. invent two situations that you think would result in distributions with similar measures of variability. explain your reasoning.
b. invent two situations that you think would result in distributions with different measures of variability. explain your reasoning.

Explanation:

Step1: Identify measures for center and variability

For a non - symmetric data set like heart rate data, median is a better measure of center as it is not affected by outliers. Inter - quartile range (IQR) is a good measure of variability for non - symmetric data as it is also robust to outliers.

Step2: Compare typical heart rates

To find the typical heart rate (center), we can look at the median. By visual inspection of the dot - plots, we can estimate the median. For situation A, the data seems to be centered around 85 - 90. For situation B, the data seems centered around 80 - 85. So situation A has a greater typical heart rate.

Step3: Compare variability

To compare variability, we can look at the spread of the data. The spread of the data in situation B seems larger as the dots are more spread out from the center compared to situation A. So situation B has greater variability.

Step4: Invent similar variability situations

Situation 1: Measuring the time it takes for students to solve two similar math problems of moderate difficulty. Since the problems are similar in nature and difficulty, the spread of the times (variability) might be similar as students' math abilities for this type of problem are likely to have a consistent spread. Situation 2: Measuring the height of apple trees in two adjacent orchards that have similar soil and climate conditions. The environmental factors being similar, the variability in tree heights might be similar.

Step5: Invent different variability situations

Situation 1: Measuring the time it takes for students to solve a very easy math problem and a very difficult math problem. The easy problem will have a small spread as most students will finish quickly, while the difficult problem will have a large spread as students' abilities vary greatly in solving difficult problems. Situation 2: Measuring the height of trees in a well - maintained orchard and a wild forest. The well - maintained orchard will have less variability in tree heights due to controlled growing conditions, while the wild forest will have a large variability due to different competition for resources, sunlight etc.

Answer:

a. Measure of center: Median; Measure of variability: Inter - quartile range (IQR). Reasoning: The data is likely non - symmetric, and median and IQR are robust to outliers.
b. Situation A
c. Situation B
2a. Situation 1: Measuring time to solve two similar moderate - difficulty math problems. Reason: Similar problem nature leads to similar ability spread. Situation 2: Measuring height of apple trees in adjacent orchards with similar conditions. Reason: Similar environment leads to similar growth variability.
2b. Situation 1: Measuring time to solve an easy and a difficult math problem. Reason: Difference in problem difficulty leads to different ability - related spread. Situation 2: Measuring height of trees in a well - maintained orchard and a wild forest. Reason: Difference in growing conditions leads to different variability.