Chapter 4: Central Tendency and Variability

Question 1

Central Tendency

Answer 1

Refers to the descriptive statistic that best represents the center of a data set, the particular value that all the other data seem to be gathering around; what we mean when we refer to the “typical score”

Question 2

Measures of central tendency

Answer 2

Mean, Median, Mode

Question 3

Mean

Answer 3

Arithmetic average of a group of scores, often called the average, used to represent the typical score in a distribution; visual point that perfectly balances two sides of a distribution

Question 4

Statistics

Answer 4

Numbers based on samples

Question 5

Parameters

Answer 5

Numbers based on populations

Question 6

To calculate the mean

Answer 6

1. Add all the scores together

2. Divide the sum of all scores by the total number of scores

Question 7

Median

Answer 7

The middle score of all the scores in a sample when the scores are arranged in ascending order

Question 8

To determine the median

Answer 8

1. Line up scores in ascending order

2. Find the middle score

Question 9

Mode

Answer 9

The easiest measure of central tendency to calculate; it is the most common score of all the scores in a sample

Question 10

Outliers and the Mean

Answer 10

When there is an outlier, sometimes,the mean is not representative of any one actual score especially if there is a small number of observations

Question 11

The Mean without the Outlier

Answer 11

When the outlier is omitted, the mean may not be more representative of the actual scores in the sample

Question 12

Which Measure of Central Tendency is Best

Answer 12

The mean is the measure of choice. However, whenever the distribution is skewed by an outlier (or when the distribution itself is skewed), the median is used to measure central tendency

Question 13

Mode

Answer 13

Used in three situations: (1) when one particular score dominates a distribution (2) when the distribution is bimodal or multimodal (3) when the data are nominal

Question 14

How to tell if you are being misled by a report of central tendency

Answer 14

1. Notice whether it is reporting an average (mean) or a median
2. If it is reporting a mean, think about whether that distribution is likely to be skewed by one extremely high number

Question 15

Variability

Answer 15

Second most common concept used to help us understand the shape of a distribution; numerical way of describing how much spread there is in a distribution

Question 16

Common indicators of variability

Answer 16

Range, Variance, and Standard Deviation

Question 17

Range

Answer 17

A way to numerically describe the variability of a distribution; measure of variability calculated by subtracting the lowest score (minimum) from the highest score (the maximum)

Question 18

Variance

Answer 18

Another way to describe the variability of a distriution

Question 19

Standard Deviation

Answer 19

The computation of the variance and its square root

Question 20

To compute Range

Answer 20

1. Determine highest score
2. Determine lowest score
3. Subtract lowest score from highest score

Question 21

Variance

Answer 21

Average of the squared deviations from the mean; describes the degree to which a distribution varies with respect to the mean

Question 22

Deviation from the mean

Answer 22

The amount that a score in a sample differs from the mean of the sample, also called deviation

Question 23

Sum of squares

Answer 23

Sum of each score’s squared deviation from the mean

Question 24

Standard Deviation

Answer 24

Square root of the average of the squared deviations from the mean; typical amount each score varies, or deviates, from the mean.

Question 25

Steps to compute standard deviation

Answer 25

1. Subtract the mean from every score
2. Square every deviation from the mean
3. Sum all of the squared deviations
4. Divide the sum of squares by the total number in the sample (N)

Question 26

Interquartile Range

Answer 26

Measure of the distance between the first and third quartiles

Question 27

First quartile

Answer 27

Marks the 25th percentile of a data set

Question 28

Third Quartile

Answer 28

Marks the 75th percentile of a data set