Description

Chamberlain University

MATH 225N: Statistical Reasoning for Health Sciences

Week 3: Distribution Shape

Question

Given the following histogram, decide if the data is skewed or symmetrical.

A histogram has a horizontal axis labeled Values from 12 to 20 in increments of 1 and a vertical axis labeled Frequency from 0 to 450 in increments of 50. The histogram has vertical bars of width 1, starting at the horizontal axis value of 13.5. The approximate heights of the bars are as follows, where the horizontal axis label is listed first and the approximate height is listed second: 13.5, 10; 14.5, 30; 15.5, 80; 16.5, 200; 17.5, 270; 18.5, 400.

• The data are skewed to the left.

 

• The data are skewed to the right.

 

• The data are symmetric.

Answer Explanation

Correct answer:

The data are skewed to the left.

Note that the histogram has most of its values concentrated on the right, with several much smaller values on the left. Therefore, the data are skewed left.

Question

Which of the following frequency tables shows a skewed data set? Select all answers that apply.

Value	Frequency
7	4
8	8
9	12
10	16
11	15
12	13
13	10
14	5

Value	Frequency
5	3
6	3
7	8
8	12
9	15
10	19
11	19
12	10
13	4
14	3
15	3
16	1

Value	Frequency
12	1
13	2
14	3
15	13
16	10
17	26
18	25
19	15
20	5

Value	Frequency
0	9
1	21
2	23
3	18
4	15
5	9
6	3
7	2

Answer Explanation

Correct answer:

Value	Frequency
12	1
13	2
14	3
15	13
16	10
17	26
18	25
19	15
20	5
Value	Frequency
0	9
1	21
2	23
3	18
4	15
5	9
6	3
7	2

Remember that data are left skewed if there is a main concentration of large values with several much smaller values. Similarly, right skewed data have a main concentration of small values with several much larger values. We can see that the following is left skewed because of the concentration of large values with many smaller values:

Value	Frequency
12	1
13	2
14	3
15	13
16	10
17	26
18	25
19	15
20	5

And the following is right skewed because of its concentration of small values with many larger values:

Value	Frequency
0	9
1	21
2	23
3	18
4	15
5	9
6	3
7	2

The other frequency tables are more balanced and symmetrical.

Question

Which of the following frequency tables show a skewed data set? Select all answers that apply.

Value	Frequency
5	2
6	5
7	9
8	15
9	18
10	24
11	19
12	15
13	10
14	4

Value	Frequency
13	2
14	5
15	14
16	13
17	23
18	26
19	15
20	2

Value	Frequency
5	1
6	1
7	9
8	20
9	24
10	20
11	9
12	4
13	1
14	1
15	1

Value	Frequency
0	4
1	12
2	23
3	28
4	17
5	7
6	6
7	3

Answer Explanation

Correct answer:

Value	Frequency
13	2
14	5
15	14
16	13
17	23
18	26
19	15
20	2
Value	Frequency
0	4
1	12
2	23
3	28
4	17
5	7
6	6
7	3

Remember that data are left skewed if there is a main concentration of large values with several much smaller values. Similarly, right skewed data have a main concentration of small values with several much larger values. We can see that the following is left skewed because of the concentration of large values with many smaller values:

Value	Frequency
13	2
14	5
15	14
16	13
17	23
18	26
19	15
20	2

And the following is right skewed because of its concentration of small values with many larger values:

Value	Frequency
0	4
1	12
2	23
3	28
4	17
5	7
6	4
7	3

The other frequency tables are more balanced and symmetrical.

Question

Which of the following frequency tables show a skewed data set? Select all answers that apply.

Value	Frequency
0	2
1	11
2	30
3	22
4	15
5	12
6	6
7	1
8	1

Value	Frequency
4	1
5	2
6	3
7	7
8	19
9	17
10	17
11	15
12	12
13	4
14	1
15	2

Value	Frequency
13	1
14	6
15	9
16	15
17	27
18	28
19	10
20	4

Value	Frequency
3	1
4	0
5	1
6	5
7	9
8	12
9	12
10	18
11	12
12	17
13	11
14	0
15	1
16	0
17	1

Answer Explanation

Correct answer:

Value	Frequency
0	2
1	11
2	30
3	22
4	15
5	12
6	6
7	1
8	1
Value	Frequency
13	1
14	6
15	9
16	15
17	27
18	28
19	10
20	4

Remember that data are left skewed if there is a main concentration of large values with several much smaller values. Similarly, right skewed data have a main concentration of small values with several much larger values. We can see that the following is left skewed because of the concentration of large values with many smaller values:

Value	Frequency
13	1
14	6
15	9
16	15
17	27
18	28
19	10
20	4

And the following is right skewed because of its concentration of small values with many larger values:

Value	Frequency
0	2
1	11
2	30
3	22
4	15
5	12
6	6
7	1
8	1

The other frequency tables are more balanced and symmetrical.

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