Chapter 3

Question 1

Population Mean

Answer 1

Sum of all values in population divided by number of values in the population.

Question 2

Parameter

Answer 2

Characteristic of a population

Question 3

Sample Mean

Answer 3

Sum of all the values in the sample divided by the number of values in the sample.

Question 4

Statistic

Answer 4

A characteristic of a sample

Question 5

First property of the Arithmetic Mean

Answer 5

Every set of interval- or ratio-level data has a mean.

Question 6

Second property of the Arithmetic Mean

Answer 6

All the values are included in computing the mean.

Question 7

Third property of the Arithmetic Mean

Answer 7

The mean is unique.

Question 8

Fourth property of the Arithmetic Mean

Answer 8

The sum of the deviations of each value from the mean is zero.

Question 9

Weighted mean

Answer 9

Special case of the arithmetic mean. It occurs when there are several observations of the same value.

Question 10

Median

Answer 10

The midpoint of the values after they have been ordered from the smallest to the largest, or the largest to the smallest.

Question 11

The two major properties of the median are:

Answer 11

1. It is not affected by extremely large or small values.

2. It can be computed for ordinal-level data or higher.

Question 12

Mode

Answer 12

The value of the observation that appears most frequently.

Question 13

T/F A skewed distribution is symmetrical

Answer 13

False. A skewed distribution is NOT symmetrical.

Question 14

For a symmetric, mound-shaped distribution, mean, median, and mode are _____.

Answer 14

equal

Question 15

In a positively skewed distribution, the arithmetic mean is the _______ of the three measures.
(lowest/largest)

Answer 15

largest

Question 16

In a negatively skewed distribution, the arithmetic mean is the _______ of the three measures.
(lowest/largest)

Answer 16

lowest

Question 17

In a highly skewed distribution, mean, median, mode are typically in which order?

Answer 17

Mean, median, and mode, starting on the positive or negative side of the respectively positive or negatively skewed distribution.

Question 18

Largest value - Smallest value =

Answer 18

Range

Question 19

The simplest measure of dispersion is ______.

Answer 19

Range

Question 20

Mean Deviation

Answer 20

The arithmetic mean of the absolute values of the deviations from the arithmetic mean.

Question 21

Population Variance

Answer 21

The arithmetic mean of the squared deviations from the mean.

Question 22

Population Standard Deviation

Answer 22

The square root of the variance.

Question 23

What is the process for finding the population variance?

Answer 23

Begin by finding the mean,
Next we find the difference between each observation and the mean and square that difference.
Then we sum all the squared differences
Finally we divide the sum of the squared differences by the number of items in the population

Question 24

How is the Sample Variance formula different than population variance?

Answer 24

Instead of a denominator of N, we have a denominator of n-1. (This is the same with Sample Standard Deviation.)

Question 25

Chebyshev’s Theorem

Answer 25

For any set of observations (sample or population), the proportion of the values that lie within k standard deviations of the mean is at least 1 - 1/(k^2), where k is any constant greater than 1.

Question 26

At least what percentage of values, according to Chebyshev’s theorem, will appear between the mean plus or minus two standard deviations of the mean?

Answer 26

75%

Question 27

At least what percentage of values, according to Chebyshev’s theorem, will appear between the mean plus or minus three standard deviations of the mean?

Answer 27

88.9%

Question 28

At least what percentage of values, according to Chebyshev’s theorem, will appear between the mean plus or minus five standard deviations of the mean?

Answer 28

96%

Question 29

Empirical Rule

Answer 29

For a symmetrical, bell-shaped frequency distribution, approximately 68% of the observations will lie within plus and minus one standard deviation of the mean; about 95% of the observations will lie within plus and minus two standard deviations of the mean; and practically all (99.7%) will lie within plus and minus three standard deviations of the mean.

Question 30

To approximate the standard deviation you can:

Answer 30

Divide the range by 6.