Question

Please Help Me!

1. Two baseball coaches recorded the number of hits each player had during practice. They displayed the results in the box plots below. The coaches determined the mean and MAD from the raw data and used that information to compare the two plots. They determined there is more variability in the number of hits per player on Team 2 than on Team 1. Which best describes this conclusion?

Inaccurate. The data sets are not symmetrical and the ranges of the two teams’ data are the same.

Accurate. The data sets are not symmetrical. There is more variability on Team 2 than on Team 1 because the median of Team 2 is greater than the median of Team 1.

Inaccurate. The data sets are not symmetrical. There is less variability on Team 2 than on Team 1 because the IQR of Team 2 is less than the IQR of Team 1.

Accurate. The data sets are not symmetrical. The MAD for Team 2 was calculated to be a larger number than the MAD for Team 1.

Answer 1

For the first option, the range is a measure of variability which measures the spread of the data set from the least value to the greatest value, but it does not take into account the variability of the other data values of the data set. The range is easily affected by the presence of outliers (data points that are away from other data points). Thus the range is regarded as a weak measure of variability and is not used when other measures of variability are available. Thus, that the range of the two data sets are equal does not mean that the data sets have the same variability. Therefore, the first option is not the correct answer.

For the second option, the median is not a measure of variability. Thus, that a data set has a greater median than another data set does not mean that the data set would have a greater variability. Therefore, the second option is not the correct answer.
For the third option, the inter-quartile range (IQR) is a better measure of variability than the range because it takes into account more data points than the range. Now, because, the the IQR of Team 2 is less than the IQR of Team 1, this shows that Team 1 have greater variability than Team 2 and thus the conclusion of the coaches are inaccurate. Therefore, the third option is the correct answer.

For the fourth option, the mean absolute deviation, MAD, is a better measure of variability than the IQR because it takes into account all the points of the data set. While IQR measures variability with respect to the median, MAD measures variability with respect to the mean. Because we are told that the data sets are not symmetrical, the median will be a better measure of the center than the mean, thus the IQR will present a better measure of the variability of the data sets. Thus, though the MAD for Team 2 was calculated to be a larger number than the MAD for Team 1, the information can be misleading in arriving at a conclusion on which data set has more variability because the data sets are not symmetrical. Therefore, the fourth option is not the correct answer.

Answer 2

Answer: C

Step-by-step explanation: it’s C