Question

2a determine the best measure of center and measure of variability to use based on the shape of the distribution. mean and standard deviation median and interquartile range distribution 2a 2b explain your thinking distribution 2b which set has the greatest measure of center? 2a (top) 2b (bottom) which set has the greatest measure of variability?

Explanation:

Step1: Analyze distribution 2a

Distribution 2a appears symmetric. For symmetric distributions, the mean and standard - deviation are the best measures of center and variability as they take into account all data points.

Step2: Analyze distribution 2b

Distribution 2b is skewed. For skewed distributions, the median and inter - quartile range are more appropriate as they are not affected by extreme values.

Step3: Compare measures of center

To compare the measures of center, we need to estimate. Visually, the center of distribution 2b is higher than that of 2a. So 2b has a greater measure of center.

Step4: Compare measures of variability

Visually, the spread of distribution 2a is larger than that of 2b. So 2a has a greater measure of variability.

Answer:

2a: mean and standard deviation
2b: median and interquartile range
Which set has the greatest measure of center? 2b (bottom)
Which set has the greatest measure of variability? 2a (top)