Question

1 twenty students participated in a psychology experiment that measured their heart rates in two different situations. (dot plots for situation a and 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: Check for outliers

Situation A has a low outlier (~75) and high outlier (~100); Situation B has no obvious outliers.

Step2: Choose center measures

For skewed data/outliers: median. For symmetric data: mean. Both can use median for consistency.

Step3: Choose variability measures

For median: interquartile range (IQR). For mean: standard deviation. IQR is robust to outliers.

Step4: Compare typical heart rates

Median of Situation A: ~87.5; Median of Situation B: ~85. Situation A’s median is higher.

Step5: Compare variability

Situation B’s data spans ~70-100; Situation A spans ~75-100 but has outliers. Situation B has wider spread.

Answer:

a. Median (center) and IQR (variability); median/IQR are robust to outliers in Situation A, consistent for both.
b. Situation A
c. Situation B
2a. Example: Heart rates during resting (Sit1) and slow walking (Sit2); both low-intensity, similar spread.
2b. Example: Heart rates during resting (Sit1) and sprinting (Sit2); sprinting has more varied effort, wider spread.