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StatisticsEssentials Of StatisticsSOCA variety of information has been gathered from a sample of college freshmen and seniors, including • Their region of birth; • The extent to which they support legalization of marijuana (measured on a scale on which 7 = strong support, 4 = neutral, and 1 = strong opposition); • The amount of money they spend each week out-of-pocket for food, drinks, and entertainment; • How many movies they watched in their dorm rooms last week; • Their opinion of cafeteria food (10 = excellent, 0 = very bad); and • Their religious affiliation. Some results are presented here. Find the most appropriate measure of central tendency for each variable for freshmen and then for seniors. Report both the measure you selected and its value for each variable (e, g., “Mode = 3” or ‘Median = 3.5”). ( HINT: Determine the level of measurement for each variable first. In general, this will tell you which measure of central tendency is appropriate. See the section “Choosing a Measure of Central Tendency” to review the relationship between measure of central tendency and level of measurement. Also, remember that the mode is the most common score, and especially remember to array scores from high to low before find the median. ) Freshmen Student Region of Birth Legalization Out-of-Pocket Expenses Movies Cafeteria Food Religion A North 7 43 0 10 Protestant B North 4 49 14 7 Protestant C South 3 55 10 2 Catholic D Midwest 2 57 7 1 None E North 3 72 5 8 Protestant F North 5 58 1 6 Jew G South 1 62 0 10 Protestant H South 4 75 14 0 Other I Midwest 1 61 3 5 Other J West 2 53 4 6 Catholic Seniors Student Region of Birth Legalization Out-of-Pocket Expenses Movies Cafeteria Food Religion K North 7 75 0 1 None L Midwest 6 72 5 2 Protestant M North 7 70 11 8 Protestant N North 5 95 3 4 Catholic O South 1 72 4 3 Protestant P South 5 67 14 6 Protestant Q West 6 50 0 2 Catholic R West 7 59 7 9 None T West 5 95 3 7 Other U North 4 88 5 4 NoneBuyFind*arrow_forward*

4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 3, Problem 3.1P

Textbook Problem

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SOCA variety of information has been gathered from a sample of college freshmen and seniors, including

• Their region of birth;

• The extent to which they support legalization of marijuana (measured on a scale on which 7 = strong support, 4 = neutral, and 1 = strong opposition);

• The amount of money they spend each week out-of-pocket for food, drinks, and entertainment;

• How many movies they watched in their dorm rooms last week;

• Their opinion of cafeteria food (10 = excellent, 0 = very bad); and

• Their religious affiliation.

Some results are presented here. Find the *most appropriate* measure of central tendency for each variable for freshmen and then for seniors. Report both the measure you selected and its value for each variable (e, g., “Mode = 3” or ‘Median = 3.5”). (*HINT: Determine the level of measurement for each variable first. In general, this will tell you which measure of central tendency is appropriate. See the section “Choosing a Measure of Central Tendency” to review the relationship between measure of central tendency and level of measurement. Also, remember that the mode is the most common score, and especially remember to array scores from high to low before find the median.*)

Freshmen |
||||||

Student | Region of Birth | Legalization | Out-of-Pocket Expenses | Movies | Cafeteria Food | Religion |

A | North | 7 | 43 | 0 | 10 | Protestant |

B | North | 4 | 49 | 14 | 7 | Protestant |

C | South | 3 | 55 | 10 | 2 | Catholic |

D | Midwest | 2 | 57 | 7 | 1 | None |

E | North | 3 | 72 | 5 | 8 | Protestant |

F | North | 5 | 58 | 1 | 6 | Jew |

G | South | 1 | 62 | 0 | 10 | Protestant |

H | South | 4 | 75 | 14 | 0 | Other |

I | Midwest | 1 | 61 | 3 | 5 | Other |

J | West | 2 | 53 | 4 | 6 | Catholic |

Seniors |
||||||

Student | Region of Birth | Legalization | Out-of-Pocket Expenses | Movies | Cafeteria Food | Religion |

K | North | 7 | 75 | 0 | 1 | None |

L | Midwest | 6 | 72 | 5 | 2 | Protestant |

M | North | 7 | 70 | 11 | 8 | Protestant |

N | North | 5 | 95 | 3 | 4 | Catholic |

O | South | 1 | 72 | 4 | 3 | Protestant |

P | South | 5 | 67 | 14 | 6 | Protestant |

Q | West | 6 | 50 | 0 | 2 | Catholic |

R | West | 7 | 59 | 7 | 9 | None |

T | West | 5 | 95 | 3 | 7 | Other |

U | North | 4 | 88 | 5 | 4 | None |

Expert Solution

To determine

**a. To find:**

The percentages of the respondents in each complex are married

**Solution:**

Variable | Measure | Freshmen | Seniors |

Region of birth | Mode | North | North |

Legalization | Median | 3 | 5 |

Expenses | Mean | 58.5 | 72.55 |

Movies | Mean | 5.80 | 5.18 |

Food | Median | 6 | 4 |

Religion | Mode | Protestant | Protestant, None |

**Description:**

When the variables measured have non-numerical scores or categories, they are said to have a nominal level of measurement.

When the variables measured have non-numerical scores or categories that could be ranked from high to low, they are said to have an ordinal level of measurement.

When the variables measured have numerical scores and can be used for further statistical analysis, they are said to have an interval ratio level of measurement.

From the given information, there are six variables **Region of Birth**, **Legalization**, **% College Bound**, **Out-of-Pocket Expenses**, **Movies, Cafeteria Food**, and **Religion**. Here, the variables **Out-of-Pocket Expenses** and **Movies** have a numeric value; therefore, the level of measurement of these variables is interval-ratio. The variables **Region of Birth** and **Religion** can be classified into categories; therefore, the level of measurement of these variables is Nominal. Further, the variables **legalization and Cafeteria Food** can be classified into categories and can be ranked; therefore, the level of measurement is Ordinal.

**Choosing a Measures of Central Tendency**

When the data is Nominal type — Mode

When the data is Ordinal type — Median

When the data is Interval ratio type — Mean

**Freshmen:**

For the variable **Out-of-Pocket Expenses, the measure of central tendency is: Mean**

**Formula Used:**

The formula to calculate mean is given by,

Substitute 10 for

For the variable **Movies, the measure of central tendency is: Mean**

**Formula Used:**

The formula to calculate mean is given by,

Substitute 10 for

For the variable **Region of Birth, the measure of central tendency is: Mode.**

**Formula used:**

**The Mode:**

The mode of any distribution of scores is the value that occurs most frequently.

In the data: “North” occurs for most frequently. Therefore, the mode is “North”.

For the variable, **Religion, the measure of central tendency is: Mode.**

**Formula used:**

**The Mode:**

The mode of any distribution of scores is the value that occurs most frequently.

In the data: “Protestant” occurs for most frequently. Therefore, the mode is “Protestant”.

For the variable **Legalization, the measure of central tendency is: Median.**

Arrange the data in the increasing order.

The data in increasing order is given by,

1 |
1 |
2 |
2 |
3 |
3 |
4 |
4 |
5 |
7 |

The formula to calculate median for even number of terms is given by,

Substitute 10 for

The value corresponding to

The required median is,

For the variable **Cafeteria Food, the measure of central tendency is: Median.**

Arrange the data in the increasing order.

The data in increasing order is given by,

0 | 1 | 2 | 5 | 6 | 6 | 7 | 8 | 10 | 10 |

The formula to calculate median for even number of terms is given by,

Substitute 10 for

The value corresponding to

The required median is,

**Seniors:**

For the variable **Out-of-Pocket Expenses, the measure of central tendency is: Mean**

**Formula Used:**

The formula to calculate mean is given by,

Substitute 11 for

For the variable **Movies, the measure of central tendency is: Mean**

**Formula Used:**

The formula to calculate mean is given by,

Substitute 11 for

For the variable **Region of Birth, the measure of central tendency is: Mode.**

**Formula used:**

**The Mode:**

The mode of any distribution of scores is the value that occurs most frequently.

In the data: “North” occurs for most frequently. Therefore, the mode is “North”.

For the variable, **Religion, the measure of central tendency is: Mode.**

**Formula used:**

**The Mode:**

The mode of any distribution of scores is the value that occurs most frequently.

In the data: “Protestant” and “None” occurs for most frequently. Therefore, the mode is “Protestant” and “None”.

For the variable **Legalization, the measure of central tendency is: Median.**

The ordered data is:

1 | 3 | 4 | 5 | 5 | 5 | 6 | 6 | 7 | 7 | 7 |

The number of terms is 11, which is odd.

The median for the odd number of terms is given by,

Substitute 11 for number of terms in the above mentioned formula,

The median corresponding to

Therefore, the median is 5.

For the variable **Cafeteria Food, the measure of central tendency is: Median.**

The ordered data is:

1 | 2 | 2 | 3 | 4 | 4 | 4 | 6 | 7 | 8 | 9 |

The number of terms is 11, which is odd.

The median for the odd number of terms is given by,

Substitute 11 for number of terms in the above mentioned formula,

The median corresponding to

Therefore, the median is 5.

Therefore,

Variable | Measure | Freshmen | Seniors |

Region of birth | Mode | North | North |

Legalization | Median | 3 | 5 |

Expenses | Mean | 58.5 | 72.55 |

Movies | Mean | 5.80 | 5.18 |

Food | Median | 6 | 4 |

Religion | Mode | Protestant | Protestant, None |

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