Chapter 4, Problem 4.4P

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4th Edition

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ISBN: 9781305093836

Textbook Problem

Respondent | Age | Attitude on Abortion (High score = Strong Opposition) |

A | 18 | 10 |

B | 20 | 9 |

C | 21 | 8 |

D | 30 | 10 |

E | 25 | 7 |

F | 26 | 7 |

G | 19 | 9 |

H | 29 | 6 |

I | 31 | 10 |

J | 55 | 5 |

K | 32 | 4 |

L | 28 | 3 |

M | 23 | 2 |

N | 24 | 1 |

O | 32 | 9 |

**3.5**
__ __ Data have been gathered on four variables for 15 respondents (see the following table). Find and report the appropriate measure of central tendency for each variable. (On the “Attitude on Abortion” scale, a high score indicates strong opposition.)

Respondent | Marital Status | Racial/Ethnic Group | Age | Attitude on Abortion |

A | Single | White | 18 | 10 |

B | Single | Hispanic | 20 | 9 |

C | Widowed | White | 21 | 8 |

D | Married | White | 30 | 10 |

E | Married | Hispanic | 25 | 7 |

F | Married | White | 26 | 7 |

G | Divorced | Black | 19 | 9 |

H | Widowed | White | 29 | 6 |

I | Divorced | White | 31 | 10 |

J | Married | Black | 55 | 5 |

K | Widowed | Asian American | 32 | 4 |

L | Married | Native American | 28 | 3 |

M | Divorced | White | 23 | 2 |

N | Married | White | 24 | 1 |

O | Divorced | Black | 32 | 9 |

To determine

**To find:**

The range and standard deviation of each given variable

Explanation

**Given:**

The following table gives the data on two variables for 15 respondents.

Respondent | Age | Attitude on Abortion (High score = Strong Opposition) |

A | 18 | 10 |

B | 20 | 9 |

C | 21 | 8 |

D | 30 | 10 |

E | 25 | 7 |

F | 26 | 7 |

G | 19 | 9 |

H | 29 | 6 |

I | 31 | 10 |

J | 55 | 5 |

K | 32 | 4 |

L | 28 | 3 |

M | 23 | 2 |

N | 24 | 1 |

O | 32 | 9 |

**Formula used:**

The formula to calculate range is given by,

Let the data values be

The formula to calculate mean is given by,

The formula to calculate standard deviation is given by,

Where,

**Calculation:**

For the variable age - arrange the data in the increasing order.

The data in increasing order is given by,

The highest age is 55 and the lowest age is 18.

The range is given by,

Substitute 55 for highest age and 18 for lowest age in the above mentioned formula,

The size of the population is 15.

The mean is given by,

Substitute 15 for

Consider the following table of sum of squares,

Scores |
||

18 | 90.8209 | |

20 | 56.7009 | |

21 | 42.6409 | |

30 | 2.47 | 6.1009 |

25 | 6.4009 | |

26 | 2.3409 | |

19 | 72.7609 | |

29 | 1.47 | 2.1609 |

31 | 3.47 | 12.0409 |

55 | 27.47 | 754.601 |

32 | 4.47 | 19.9809 |

28 | 0.47 | 0.2209 |

23 | 20.5209 | |

24 | 12.4609 | |

32 | 4.47 | 19.9809 |

From equation

Square the both sides of the equation.

Proceed in the same manner to calculate

The standard deviation is given by,

From equation

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