Lesson 4
The Shape of 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=20240727T023520Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=60d00f4ca95efc356d7f0eeb468bdfd5860b76b04a021246cf85137377025a4e)
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=20240727T023520Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c2bd43cfe67a3f58f635574ea280f82e55b34741f6ee1985b0c739e9cdf5e600)
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=20240727T023520Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4c299ef82bfeecf2cda9ce9510312d9c0c5623178440818f0f732b4825391ed5)
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=20240727T023520Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d7545d2e71e41e62fd8841ecb095e2615d2173ba042118847a58d15e8d6c8b64)
Solution
For access, consult one of our IM Certified Partners.
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=20240727T023520Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c56728aed6e386b39c125e1157013d40e4e30380b7ddb15ce5bed174f3b13441)
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=20240727T023520Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=57db2519f09a37e589fd157ea2ba04044c291225e0bc0734367056729502b787)
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=20240727T023520Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=999ca7678ae1a53b7f8f2e1498512018f1f3e6a12e1da97abb9c388ee3090a06)
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=20240727T023520Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=87dc9affeb18a0f33a6c755e4021c063f7664e479ae70429086c1f32aa18e5d4)
Solution
For access, consult one of our IM Certified Partners.
Problem 3
Create a dot plot showing a uniform distribution.
Solution
For access, consult one of our IM Certified Partners.
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?
Solution
For access, consult one of our IM Certified Partners.
(From Unit 1, Lesson 3.)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?
Solution
For access, consult one of our IM Certified Partners.
(From Unit 1, Lesson 2.)