A paper gave summary quantities for blood lead level (in micrograms per deciliter) for a sample of whites and a sample of African Americans. Data consistent with the given summary quantities is given below. Whites (W) 8.3 0.9 2.9 5.6 5.8 5.4 1.2 1.0 1.4 2.1 1.3 5.3 8.4 6.6 5.2 3.4 2.9 2.7 6.7 3.6 African Americans (AA) 4.8 1.4 0.9 10.8 2.4 0.6 5.0 5.4 6.1 2.9 5.0 2.1 7.5 3.4 13.6 1.4 3.7 3.3 14.8 3.9 (a) Calculate the values of the mean and the median for blood lead level for the sample of African Americans. mean median (b) Which of the mean or the median is larger? What characteristic of the data set explains the relative values of the mean and the median? The median is greater than the mean. This is explained by the fact that the distribution is positively skewed. The mean is greater than the median. This is explained by the fact that the distribution is positively skewed. The median is greater than the mean. This is explained by the fact that the distribution is negatively skewed. The mean is greater than the median. This is explained by the fact that the distribution is negatively skewed. (c) Construct a comparative boxplot for blood lead level for the two samples. The box-and-whisker plot has a vertical axis numbered from 0 to 15. The box-and-whisker is also vertical. The boxplot labeled "AA" occurs next. The bottom whisker is approximately 0.9, the bottom edge of the box is approximately 1.75, the line inside the box is approximately 3.5, the top edge of the box is approximately 5.7, and the top whisker is approximately 8.4. The boxplot labeled "W" occurs next. The bottom whisker is approximately 0.6, the bottom edge of the box is approximately 2.25, the line inside the box is approximately 3.8, the top edge of the box is approximately 5.75, and the top whisker is approximately 10.8. There are 2 outliers located at 13.6 and 14.8. The box-and-whisker plot has a vertical axis numbered from 0 to 15. The box-and-whisker is also vertical. The boxplot labeled "AA" occurs next. The bottom whisker is approximately 1.1, the bottom edge of the box is approximately 1.75, the line inside the box is approximately 4.2, the top edge of the box is approximately 5.7, and the top whisker is approximately 8.4. The boxplot labeled "W" occurs next. The bottom whisker is approximately 0.6, the bottom edge of the box is approximately 2.1, the line inside the box is approximately 4.15, the top edge of the box is approximately 5.75, and the top whisker is approximately 10.8. There are 2 outliers located at 13.6 and 14.8. The box-and-whisker plot has a vertical axis numbered from 0 to 15. The box-and-whisker is also vertical. The boxplot labeled "AA" occurs next. The bottom whisker is approximately 0.6, the bottom edge of the box is approximately 2.25, the line inside the box is approximately 3.8, the top edge of the box is approximately 5.75, and the top whisker is approximately 10.8. There are 2 outliers located at 13.6 and 14.8. The boxplot labeled "W" occurs next. The bottom whisker is approximately 0.9, the bottom edge of the box is approximately 1.75, the line inside the box is approximately 3.5, the top edge of the box is approximately 5.7, and the top whisker is approximately 8.4. The box-and-whisker plot has a vertical axis numbered from 0 to 15. The box-and-whisker is also vertical. The boxplot labeled "AA" occurs next. The bottom whisker is approximately 0.6, the bottom edge of the box is approximately 2.1, the line inside the box is approximately 4.15, the top edge of the box is approximately 5.75, and the top whisker is approximately 10.8. There are 2 outliers located at 13.6 and 14.8. The boxplot labeled "W" occurs next. The bottom whisker is approximately 1.1, the bottom edge of the box is approximately 1.75, the line inside the box is approximately 4.2, the top edge of the box is approximately 5.7, and the top whisker is approximately 8.4. (d) Write a few sentences comparing the blood lead level distributions for the two samples. (Select all that apply.) Both distributions seem to be negatively skewed. There are two outliers in the data set for the African Americans The median blood lead level for the African Americans is slightly lower than for the Whites. The median blood lead level for the African Americans is slightly higher than for the Whites.Both distributions seem to be positively skewed. The distribution for the African Americans shows a greater range than the distribution for the Whites The distribution for the Whites shows a greater range than the distribution for the African Americans.

A paper gave summary quantities for blood lead level (in micrograms per deciliter) for a sample of whites and a sample of African Americans. Data consistent with the given summary quantities is given below. Whites (W) 8.3 0.9 2.9 5.6 5.8 5.4 1.2 1.0 1.4 2.1 1.3 5.3 8.4 6.6 5.2 3.4 2.9 2.7 6.7 3.6 African Americans (AA) 4.8 1.4 0.9 10.8 2.4 0.6 5.0 5.4 6.1 2.9 5.0 2.1 7.5 3.4 13.6 1.4 3.7 3.3 14.8 3.9 (a) Calculate the values of the mean and the median for blood lead level for the sample of African Americans. mean median (b) Which of the mean or the median is larger? What characteristic of the data set explains the relative values of the mean and the median? The median is greater than the mean. This is explained by the fact that the distribution is positively skewed. The mean is greater than the median. This is explained by the fact that the distribution is positively skewed. The median is greater than the mean. This is explained by the fact that the distribution is negatively skewed. The mean is greater than the median. This is explained by the fact that the distribution is negatively skewed. (c) Construct a comparative boxplot for blood lead level for the two samples. The box-and-whisker plot has a vertical axis numbered from 0 to 15. The box-and-whisker is also vertical. The boxplot labeled "AA" occurs next. The bottom whisker is approximately 0.9, the bottom edge of the box is approximately 1.75, the line inside the box is approximately 3.5, the top edge of the box is approximately 5.7, and the top whisker is approximately 8.4. The boxplot labeled "W" occurs next. The bottom whisker is approximately 0.6, the bottom edge of the box is approximately 2.25, the line inside the box is approximately 3.8, the top edge of the box is approximately 5.75, and the top whisker is approximately 10.8. There are 2 outliers located at 13.6 and 14.8. The box-and-whisker plot has a vertical axis numbered from 0 to 15. The box-and-whisker is also vertical. The boxplot labeled "AA" occurs next. The bottom whisker is approximately 1.1, the bottom edge of the box is approximately 1.75, the line inside the box is approximately 4.2, the top edge of the box is approximately 5.7, and the top whisker is approximately 8.4. The boxplot labeled "W" occurs next. The bottom whisker is approximately 0.6, the bottom edge of the box is approximately 2.1, the line inside the box is approximately 4.15, the top edge of the box is approximately 5.75, and the top whisker is approximately 10.8. There are 2 outliers located at 13.6 and 14.8. The box-and-whisker plot has a vertical axis numbered from 0 to 15. The box-and-whisker is also vertical. The boxplot labeled "AA" occurs next. The bottom whisker is approximately 0.6, the bottom edge of the box is approximately 2.25, the line inside the box is approximately 3.8, the top edge of the box is approximately 5.75, and the top whisker is approximately 10.8. There are 2 outliers located at 13.6 and 14.8. The boxplot labeled "W" occurs next. The bottom whisker is approximately 0.9, the bottom edge of the box is approximately 1.75, the line inside the box is approximately 3.5, the top edge of the box is approximately 5.7, and the top whisker is approximately 8.4. The box-and-whisker plot has a vertical axis numbered from 0 to 15. The box-and-whisker is also vertical. The boxplot labeled "AA" occurs next. The bottom whisker is approximately 0.6, the bottom edge of the box is approximately 2.1, the line inside the box is approximately 4.15, the top edge of the box is approximately 5.75, and the top whisker is approximately 10.8. There are 2 outliers located at 13.6 and 14.8. The boxplot labeled "W" occurs next. The bottom whisker is approximately 1.1, the bottom edge of the box is approximately 1.75, the line inside the box is approximately 4.2, the top edge of the box is approximately 5.7, and the top whisker is approximately 8.4. (d) Write a few sentences comparing the blood lead level distributions for the two samples. (Select all that apply.) Both distributions seem to be negatively skewed. There are two outliers in the data set for the African Americans The median blood lead level for the African Americans is slightly lower than for the Whites. The median blood lead level for the African Americans is slightly higher than for the Whites.Both distributions seem to be positively skewed. The distribution for the African Americans shows a greater range than the distribution for the Whites The distribution for the Whites shows a greater range than the distribution for the African Americans.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Whites (W)	8.3	0.9	2.9	5.6	5.8	5.4	1.2
1.0	1.4	2.1	1.3	5.3	8.4	6.6
5.2	3.4	2.9	2.7	6.7	3.6
African Americans (AA)	4.8	1.4	0.9	10.8	2.4	0.6	5.0
5.4	6.1	2.9	5.0	2.1	7.5	3.4
13.6	1.4	3.7	3.3	14.8	3.9

(a)

Calculate the values of the mean and the median for blood lead level for the sample of African Americans.

mean

median

(b)

Which of the mean or the median is larger? What characteristic of the data set explains the relative values of the mean and the median?

The median is greater than the mean. This is explained by the fact that the distribution is positively skewed.

The mean is greater than the median. This is explained by the fact that the distribution is positively skewed.

The median is greater than the mean. This is explained by the fact that the distribution is negatively skewed.

The mean is greater than the median. This is explained by the fact that the distribution is negatively skewed.

(c)

Construct a comparative boxplot for blood lead level for the two samples.

The box-and-whisker plot has a vertical axis numbered from 0 to 15. The box-and-whisker is also vertical. The boxplot labeled "AA" occurs next. The bottom whisker is approximately 0.9, the bottom edge of the box is approximately 1.75, the line inside the box is approximately 3.5, the top edge of the box is approximately 5.7, and the top whisker is approximately 8.4. The boxplot labeled "W" occurs next. The bottom whisker is approximately 0.6, the bottom edge of the box is approximately 2.25, the line inside the box is approximately 3.8, the top edge of the box is approximately 5.75, and the top whisker is approximately 10.8. There are 2 outliers located at 13.6 and 14.8.

The box-and-whisker plot has a vertical axis numbered from 0 to 15. The box-and-whisker is also vertical. The boxplot labeled "AA" occurs next. The bottom whisker is approximately 1.1, the bottom edge of the box is approximately 1.75, the line inside the box is approximately 4.2, the top edge of the box is approximately 5.7, and the top whisker is approximately 8.4. The boxplot labeled "W" occurs next. The bottom whisker is approximately 0.6, the bottom edge of the box is approximately 2.1, the line inside the box is approximately 4.15, the top edge of the box is approximately 5.75, and the top whisker is approximately 10.8. There are 2 outliers located at 13.6 and 14.8.

The box-and-whisker plot has a vertical axis numbered from 0 to 15. The box-and-whisker is also vertical. The boxplot labeled "AA" occurs next. The bottom whisker is approximately 0.6, the bottom edge of the box is approximately 2.25, the line inside the box is approximately 3.8, the top edge of the box is approximately 5.75, and the top whisker is approximately 10.8. There are 2 outliers located at 13.6 and 14.8. The boxplot labeled "W" occurs next. The bottom whisker is approximately 0.9, the bottom edge of the box is approximately 1.75, the line inside the box is approximately 3.5, the top edge of the box is approximately 5.7, and the top whisker is approximately 8.4.

The box-and-whisker plot has a vertical axis numbered from 0 to 15. The box-and-whisker is also vertical. The boxplot labeled "AA" occurs next. The bottom whisker is approximately 0.6, the bottom edge of the box is approximately 2.1, the line inside the box is approximately 4.15, the top edge of the box is approximately 5.75, and the top whisker is approximately 10.8. There are 2 outliers located at 13.6 and 14.8. The boxplot labeled "W" occurs next. The bottom whisker is approximately 1.1, the bottom edge of the box is approximately 1.75, the line inside the box is approximately 4.2, the top edge of the box is approximately 5.7, and the top whisker is approximately 8.4.

(d)

Write a few sentences comparing the blood lead level distributions for the two samples. (Select all that apply.)

Both distributions seem to be negatively skewed.

There are two outliers in the data set for the African Americans

The median blood lead level for the African Americans is slightly lower than for the Whites.

The median blood lead level for the African Americans is slightly higher than for the Whites.Both distributions seem to be positively skewed.

The distribution for the African Americans shows a greater range than the distribution for the Whites

The distribution for the Whites shows a greater range than the distribution for the African Americans.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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