PSY201: Chapter 3 - Central Tendency

Question 1

Central Tendency

Answer 1

Goal: Identify the single value that best represents entire set of data

Question 2

Central Tendency

Answer 2

allows researchers to summarize/condense large set of data into single value
descriptive statistic - allows researchers to describe/present set of data in very simplified, concise form
possible to compare 2/more sets of data by comparing avg score (central tendency) for one set vs another set

Question 3

Measure of Central tendency: The Mean, the Median, and the Mode

Answer 3

determined by objective + well‐defined statistical procedure so others will understand exactly how avg value was obtained + can duplicate process
No single procedure always produces a good representative value

Question 4

Mean

Answer 4

Most commonly used measure of central tendency.
Computation requires scores numerical values measured
on interval/ratio scale
sum of entire set of scores, then dividing by # of scores

Question 5

Mean

Answer 5

Widespread use
sample mean better estimate of pop’s mean
But, influenced by extreme scores

Question 6

Mean

Answer 6

balance point of distribution - sum of distances below the mean = sum of distances above the mean

Question 7

Changing the Mean

Answer 7

changing any score will change value of mean

Modifying distribution by discarding scores/adding new scores will usually change value of the mean

Question 8

Changing the Mean

Answer 8

1) how # of scores affected

2) how sum of scores affected

Question 9

Changing the Mean

Answer 9

constant value added to every score ⇒ same constant added to mean
every score multiplied by constant value ⇒ mean multiplied by same constant value

Question 10

When the Mean Won’t Work

Answer 10

distribution contains few extreme scores/very skewed ⇒ mean pulled toward the extremes (displaced toward tail) mean will not provide a “central” value

Question 11

When the Mean Won’t Work

Answer 11

nominal scale - impossible to compute mean
ordinal scale (ranks) - inappropriate to compute a mean

Question 12

Weighted Mean

Answer 12

May need to find overall mean for more than one group

ΣX(overall sum)/N(total n)

Question 13

Characteristics of the Mean

Answer 13

Changing a score
Adding/subtracting a score
Multiplying/dividing a score

Question 14

Mean: Advantages

Answer 14

Calculated from all the data
Can be manipulated using an equation
Related to variance and standard
Can estimate population mean

Question 15

Mean: Disadvantages

Answer 15

Influenced by extreme scores

Value may not exist in data

Question 16

The Median

Answer 16

scores listed in order from smallest to largest - midpoint
divides scores so 50% of scores have values =/less than median
requires scores that can be placed in rank order + measured on ordinal, interval/ratio scale
Relatively unaffected by extreme scores

Question 17

The Median

Answer 17

1. With an odd number of scores, list the values in order, and the median is the middle score in the list.
2. With an even number of scores, list the values in order, and the median is half-way between the middle two scores.

Question 18

The Median

Answer 18

continuous variable, possible to find median by first placing scores in a frequency distribution histogram with each score represented by a box in the graph.
draw vertical line through distribution so exactly half boxes are on each side of the line. The median defined by the location of the line

Question 19

The Median: Advantage

Answer 19

Relatively unaffected by extreme scores

tends to stay in the “centre” of distribution even when few extreme scores or when distribution is very skewed

Question 20

The Median: Disadvantages

Answer 20

Ignores most of the data.
May not have occurred
Difficult to work with.
Not stable between samples

Question 21

The Mode

Answer 21

most frequently occurring category/score in distribution.
category/score at peak of distribution
Can be determined for data measured on any scale of measurement: nominal, ordinal, interval/ratio

Question 22

The Mode: Advantage

Answer 22

Unaffected by extreme scores
Score actually occurred
Represents largest # of scores
Only one of the 3 that can be used for nominal data.
Can be used as supplemental measure reported along with mean/median

Question 23

The Mode: Disadvantage

Answer 23

Based on only a few data points
Depends on how data grouped
Not representative of entire data set

Question 24

Bimodal Distributions

Answer 24

Possible for distribution to have more than one mode - bimodal
mode often used to describe peak not really highest point major mode at highest peak + minor mode at secondary peak in a diff location

Question 25

Which measure to use?

Answer 25

mode ⇒ data categorical + values can fit into only one class (hair colour, political affiliation)
median ⇒ have extreme scores (income in dollars)
mean ⇒ data has no extreme scores + not categorical (numerical scores on a test)

Question 26

Which measure to use?

Answer 26

Mean most precise measure, then median, + lastly mode

Use the most precise measure if possible

Question 27

When not to use…

Answer 27

mean ⇒ don’t have right data scale (nominal/ordinal), distribution not unimodal/is skewed (watch out for outliers).

Question 28

When not to use…

Answer 28

median ⇒ data is nominal/distribution not unimodal

mode ⇒ None

Question 29

Central Tendency and the Shape of the Distribution

Answer 29

3 measures often systematically related to each other

symmetrical distribution - mean + median will always be equal.

Question 30

Central Tendency and the Shape of the Distribution

Answer 30

symmetrical distribution - one mode ⇒ mode, mean + median have same value
skewed distribution ⇒ mode at peak on one side + mean usually displaced toward tail on other side
median usually located betw mean + mode

Question 31

Reporting Central Tendency in Research Reports

Answer 31

sample mean = M
no standardized notation for reporting median/mode
several means obtained for diff groups/treatment conditions, common to present all of means in a single graph

Question 32

Reporting Central Tendency in Research Reports

Answer 32

diff groups/treatment conditions - horizontal axis + means are displayed by bar/point above each of groups
height = mean for each group.
Similar graphs also used to show several medians in 1 display

Question 33

Central Tendency

Answer 33

Fails to give whole story
Need measure to indicate degree to which individual
observations clustered about/deviate from centre
centre may represent majority of scores/may be distributed over a wide range of values