3. Describing Data with Averages

Question 1

Measures of Central Tendency

Answer 1

Numbers or words that attempt to describe, most generally, the middle or typical value for a distribution.

Question 2

Mode

Answer 2

The value of the most frequent score.

Question 3

Bimodal

Answer 3

Describes any distribution with two obvious peaks.

Question 4

Multimodal

Answer 4

Describes any distribution with more than two peaks.

Question 5

Determine the mode for the following retirement ages:

60, 63, 45, 63, 65, 70, 55, 63, 60, 65, 63

Answer 5

Mode = 63

Question 6

The owner of a new car conducts six gas mileage tests and obtains the following results, expressed in miles per gallon. Find the mode for these data.

26.3, 28.7, 27.4, 26.6, 27.4, 26.9

Answer 6

Mode = 27.4

Question 7

Median

Answer 7

The middle value when observations are ordered from least to most.

Question 8

What are the 6 steps for finding the median?

Answer 8

1. Order scores from least to most.
2. Find the middle position by adding one to the total number of scores and dividing it by 2.
3. If the middle position is a whole number, use this number to count into the set of ordered scores.
4. The value of the median equals the value of the score located at the middle position.
5. If the middle position is not a whole number, use the two nearest whole numbers to count into the set of ordered scores.
6. The value of the median equals the value midway between those of the two middlemost scores; to find the midway value, add the two given values and divide by 2.

Question 9

Find the median for the following retirement ages:

60, 63, 45, 63, 65, 70, 55, 63, 60, 65, 63

Answer 9

Median = 63

Question 10

Find the median for the following gas mileage tests:

26.3, 28.7, 27.4, 26.6, 27.4, 26.9

Answer 10

Median = 27.15

Question 11

How do you find the mean?

Answer 11

The mean is found by adding all scores and then dividing by the number of scores.

Question 12

Population

Answer 12

A complete set of scores.

Question 13

Sample

Answer 13

A subset of scores.

Question 14

Sample Mean ( ̅X)

Answer 14

The balance point for a sample, found by dividing the sum for the values of all scores in the sample by the number of scores in the sample.

̅X = (∑X) / n

Question 15

Sample Size (n)

Answer 15

The total number of scores in the sample.

Question 16

Population Mean (µ)

Answer 16

The balance point for a population, found by dividing the sum for all scores in the population by the number of scores in the population.

µ = (∑X) / N

Question 17

Population Size (N)

Answer 17

The total number of scores in the population.

Question 18

Find the mean for the following retirement ages:

60, 63, 45, 63, 65, 70, 55, 63, 60, 65, 63

Answer 18

Mean = 672 / 11 = 61.09

Question 19

Find the mean for the following gas mileage tests:

26.3, 28.7, 27.4, 26.6, 27.4, 26.9

Answer 19

Mean = 163.3 / 6 = 27. 22

Question 20

Indicate whether the following skewed distribution are positively skewed or negatively skewed:

a distribution of test scores on an easy test, with most students scoring high and a few students scoring low

Answer 20

negatively skewed because the median exceeds the mean

Question 21

Indicate whether the following skewed distribution are positively skewed or negatively skewed:

a distribution of ages of college students, with most students in their late teens or early twenties and a few students in their fifties or sixties

Answer 21

positively skewed because the mean exceeds the median

Question 22

Indicate whether the following skewed distribution are positively skewed or negatively skewed:

a distribution of loose change carried by classmates, with most carrying less than $1 and with some carrying $3 or $4 worth of loose change.

Answer 22

positively skewed because the mean exceeds the median

Question 23

Indicate whether the following skewed distribution are positively skewed or negatively skewed:

a distribution of the sizes of crowds in attendance at a popular movie theater, with most audiences at or near capacity

Answer 23

negatively skewed because the median exceeds the mean

Question 24

College students were surveyed about where they would most like to spend their spring break: Daytona Beach (DB); Cancun Mexico (C), South Padre Island (SP), Lake Havasu (LH), or other (O). The results were as follows:

DB DB C LH DB
C SP LH DB O
O SP C DB LH
DB C DB O DB

Find the mode and the median.

Answer 24

Mode = DB (Daytona Beach)

Impossible to fin the median when qualitative data are unordered, with only nominal measurement.