Chapter 3: Central Tendency

Question 1

central tendency

Answer 1

A statistical measure that determines a single value that accurately describes the center of the distribution and represents the entire distribution of scores

Question 2

3 commonly used measures of central tendency

Answer 2

mean, median, mode

Question 3

mean

Answer 3

The mean is the sum of all the scores divided by the number of scores in the data

Question 4

formula for population mean

Answer 4

μ = ∑ x / N

Question 5

formula for sample mean

Answer 5

M = ∑ x / N

Question 6

calculating ∑ x given the mean and number of samples

Answer 6

∑ x = M* n

Question 7

calculating n given the sum of x and the mean

Answer 7

n= ∑ x/ M

Question 8

2 other ways to think about the mean

Answer 8

1. the mean is the amount that each individual receives when the total is divided equally
2. the mean is the balance point of the distribution because the sum of the distances below the mean is exactly equal to the sum of the distances above the mean

Question 9

weighted mean

Answer 9

a mean that takes into account different group sizes

Question 10

steps for calculating weighted mean

Answer 10

1. Determine the combined sum of all the scores
2. Determine the combined number of scores
3. Divide the sum of scores by the total number of scores

Question 11

formula for weighted mean

Answer 11

μw= ∑ x1 +∑ x2 / N1 + N2

Question 12

t or f: changing the value of one score changes the mean

Answer 12

true

Question 13

t or f: adding or removing a score changes the mean

Answer 13

true

Question 14

adding or subtracting a constant from each score does what to the mean

Answer 14

changes the mean by that same constant

Question 15

Multiplying or dividing each score by a constant does what to the mean

Answer 15

multiples or divides it by that constant

Question 16

when won’t the mean work?

Answer 16

when there are extreme scores or when the data is ordinal or nominal (non-numeric)

Question 17

median

Answer 17

the midpoint of the distribution when scores are ordered from smallest to largest

Question 18

pros of the median

Answer 18

• less affected by extreme scores
• can be used with ordinal data (ranked, but non-numeric)

Question 19

mode

Answer 19

the most frequently occurring category in the distribution

Question 20

pros of the mode

Answer 20

can be used for any scale of measurement: nominal, ordinal, interval, or ratio

Question 21

bimodal distributions

Answer 21

distributions with more than one mode

Question 22

major mode

Answer 22

the highest value in a set of data

Question 23

minor mode

Answer 23

a peak of the data that isn’t the highest point overall

Question 24

central tendency and symmetrical distributions

Answer 24

mean, median, and mode are the same

Question 25

central tendency and positively skewed distributions

Answer 25

(from smallest to largest): mode, median, mean

Question 26

central tendency and negatively skewed distributions

Answer 26

(from smallest to largest): mean, median, mode

Question 27

if the mean is larger than the median, the distribution is ___

Answer 27

positively skewed

Question 28

if the mean is smaller than the median, the distribution is ___

Answer 28

negatively skewed

Question 29

central tendency and rectangular distribution

Answer 29

no mode because all x values occur in the same frequency. the mean and the median are at the center of the distribution