Question

A poll asked 15 men in two age groups, 30 and younger and older than 30, whether they had facial hair (mustache, beard, sideburns, etc.). The results are recorded in the table.
Person | Age | Facial hair
1 30 and younger Yes
2 30 and younger No
3 Older than 30 No
4 30 and younger No
5 Older than 30 No
6 Older than 30 Yes
7 Older than 30 Yes
8 Older than 30 No
9 30 and younger Yes
10 30 and younger Yes
11 Older than 30 Yes
12 30 and younger Yes
13 Older than 30 Yes
14 30 and younger No
15 Older than 30 Yes
(a) Create a two-way table of the data. Of the men surveyed, how many were 30 and younger? How many men did not have facial hair?
(b) Create a two-way relative frequency table that displays the relative frequency of the men 30 and younger and of the men older than 30 who had or did not have facial hair. Express your answers as decimals written to three decimal places.
(c) What percentage of men older than 30 had facial hair?

Answer 1

You need to count the persons and classify them into four groups.

1) 30 and younger with facial hair: 4 people

2) older than 30 with facial hair: 5 people

3) 30 and younger without facial hair: 3

4) older than 30 without facial hair: 4

(a)

Create a two-way table of the data. Of the men surveyed, how many were

30 and younger? How many men did not have facial hair?

This is the table using the data classified:

                           --------------------------------------------------------------

                          |with facial hair    | without facial hair | total |

-------------------------------------------------------------------------------------

30 & younger     |     4                     |   3                              |  7      |

-------------------------------------------------------------------------------------

older than 30     |    5                      |   3                              |   8       |

-------------------------------------------------------------------------------------

Total                   |    9                      |   6                             |  15    |

-------------------------------------------------------------------------------------

7 men were 30 and  younger.

6 men did not have facial hair.

(b) Create a two-way relative frequency table that displays the relative

frequency of the men 30 and younger and of the men older than 30 who

had or did not have facial hair.

Express your answers as decimals

written to three decimal places.

This is the table:

                          ---------------------------------------------------------------

                          |with facial hair    | without facial hair | total  |

-------------------------------------------------------------------------------------

30 & younger     |     4/15                |   3/15 = 1/5                |  7/15  |

-------------------------------------------------------------------------------------

older than 30     |    5 /15 = 1/3      |   3/15 = 1/5                |   8/15   |

-------------------------------------------------------------------------------------

Total                  |    9/15 = 3/5        |   6/15 = 2/5                 |  1      |

-------------------------------------------------------------------------------------

This is the answer showing three decimal digits:

                          ---------------------------------------------------------------

                          |with facial hair    | without facial hair | total  |

-------------------------------------------------------------------------------------

30 & younger     |    0.267                |   0.200                |0.467  |

-------------------------------------------------------------------------------------

older than 30     |    0.333               |   0.200                |0.533   |

-------------------------------------------------------------------------------------

Total                  |      0.600              |   0.400                 |  1      |

-------------------------------------------------------------------------------------

(c) What percentage of men older than 30 had facial hair?

Percentage = relative frequency * 100 % =  (1/3)*100 % = 33.33%