Lesson 4
The Shape of Distributions
- Let’s explore data and describe distributions.
Problem 1
Which of the dot plots shows a symmetric distribution?
A: ![Dot plot from 9 to 20 by 1’s. Beginning at 9, number of dots above each increment is 0, 1, 1, 2, 3, 5, 6, 7, 8, 2, 1, 0.](https://cms-im.s3.amazonaws.com/tUfPshNjXru1EUmsWnpgaEf9?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-1015.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-1015.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T120017Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b9cf08fca0d09979f086f9bd52cce9e10417f21538730504d8109da876bd53cd)
B: ![Dot plot from 9 to 20 by 1’s. Beginning at 9, number of dots above each increment is 0, 1, 1, 2, 3, 5, 3, 2, 1, 1, 0, 0.](https://cms-im.s3.amazonaws.com/1ngNbqhLLePEFsoZtuq8b1Hz?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-1016.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-1016.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T120017Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=414ab8b3fad4a06b0fb3f560fff1d5e5cffb8051ff870c226be7b27dde9fe752)
C: ![Dot plot from 1 to 12 by 1’s. Beginning at 1, number of dots above each increment is 0, 4, 0, 6, 7, 0, 3, 0, 2, 6, 5, 0.](https://cms-im.s3.amazonaws.com/zWyMmFuwekT3BASnBXGtovQu?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-1018.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-1018.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T120017Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=55d451af459d5feaa3cfcce972d025e6bc431f02654443cdce88d04cd2e98b27)
D: ![Dot plot from 1.1 to 1.9 by 0.1’s. Beginning at 1.1, number of dots above each increment is 0, 6, 4, 2, 1, 7, 11, 15, 0.](https://cms-im.s3.amazonaws.com/iUpQxK6mbtYt95fhk6tiSi4w?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-1019.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-1019.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T120017Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=382f9d1828625d507b7a576c14b57eaddc856e0048097b7295a22a4645fa0881)
Problem 2
Which of the dot plots shows a skewed distribution?
A: ![Dot plot from 1.1 to 1.9 by 0.1’s. Beginning at 1.1, number of dots above each increment is 0, 6, 4, 2, 1, 1, 4, 6, 0.](https://cms-im.s3.amazonaws.com/TVmCfEXjBnstfMtnD5u1rMg1?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-1020.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-1020.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T120017Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=931cb7eece1aecfd0332bbb3b7983be709fd7376719fc06d4fb30a005370c967)
B: ![Dot plot from 0.5 to 6 by 0.5’s. Beginning at 0.5, number of dots above each increment is 0, 0, 0, 4, 6, 4, 1, 4, 6, 4, 0, 0.](https://cms-im.s3.amazonaws.com/G84qtcWqWNSTX8bZpRWxXXut?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-1021.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-1021.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T120017Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=624daa672aae39dbe30073172223c3cf91adcfafd91ae4ed09bbc61db19882e8)
C: ![Dot plot from 9 to 18 by 1’s. Beginning at 9, number of dots above each increment is 0, 3, 5, 7, 9, 9, 7, 5, 3, 0.](https://cms-im.s3.amazonaws.com/U47FyCfME8TgEgv7DFvLkCrJ?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-1022.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-1022.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T120017Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c0291cb1ea5bf1257bec6ca05a01cbfd8f9f9f174a580e7b728223405fa5f380)
D: ![Dot plot from 1.1 to 2.1 by 0.1’s. Beginning at 1.1, number of dots above each increment is 0, 8, 9, 6, 4, 1, 0, 1, 0.](https://cms-im.s3.amazonaws.com/eERUtTrp3q36bakdRLwv49KU?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-1023.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-1023.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T120017Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e9ed1f1ce18dd99a8b81b1bbc48c75e0852f3ebafd0d51ab34f9732fbab14f3c)
Problem 3
Create a dot plot showing a uniform distribution.
Problem 4
The data represent the number of ounces of water that 26 students drank before donating blood: 8, 8, 8, 16, 16, 16, 32, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 80, 80, 80, 80, 88, 88, 88.
- Create a dot plot for the data.
- Create a box plot for the data.
- What information about the data is provided by the box plot that is not provided by the dot plot?
- What information about the data is provided by the dot plot that is not provided by the box plot?
- It was recommended that students drink 48 or more ounces of water. How could you use a histogram to easily display the number of students who drank the recommended amount?
Problem 5
The box plot represents the distribution of the number of points scored by a cross country team at 12 meets.
- If possible, find the mean. If not possible, explain why not.
- If possible, find the median. If not possible, explain why not.
- Did the cross country team ever score 30 points at a meet?