Question

data were gathered from two groups and displayed in the histograms. compare the appropriate measures of center and variability for the two sets of data. data set a: mean = 32.125, median = 63.5, standard deviation = 22.526, iqr = 35.5. data set b: mean = 32.125, median = 31.5, standard deviation = 19.526, iqr = 37.5. data set a has a higher median value of 63.5, and data set b has a greater iqr value of 37.5. data set a has a lower median value of 63.5, and data set b has a smaller iqr value of 37.5. data set a has a lower mean value of 32.125, and data set b has a greater standard deviation value of 19.526. data set a has a higher mean value of 32.125, and data set b has a smaller standard deviation value of 19.526.

Explanation:

Step1: Identify measures of center and variability

Measures of center are mean and median. Variability measures are standard - deviation and IQR.

Step2: Compare means

Data Set A mean = 32.125, Data Set B mean = 33.427. So Data Set B has a higher mean.

Step3: Compare medians

Data Set A median = 63.5, Data Set B median = 31.5. So Data Set A has a higher median.

Step4: Compare standard - deviations

Data Set A standard deviation = 22.526, Data Set B standard deviation = 19.526. So Data Set A has a higher standard deviation.

Step5: Compare IQRs

Data Set A IQR = 35.5, Data Set B IQR = 37.5. So Data Set B has a higher IQR.

Answer:

Data Set A has a higher median value of 63.5, and Data Set B has a greater IQR value of 37.5.