Descriptive Statistics: Measures of Central Tendency

Question 1

what is descriptive statistics?

Answer 1

numbers that summarize a set of data

Question 2

what are two common ways/types of descriptive statistics?

Answer 2

1. measures of central tendency

2. measures of variability

Question 3

what is central tendency

Answer 3

a measure of the “typical” value in a collection of numbers or a data set

Question 4

mean

Answer 4

sum of all scores divided by total (keep two decimal places)

Question 5

pro’s and con’s of mean:

Answer 5

pro: most common statistics, easily manipulated algebraically
con: greatly affected by extreme scores/outliers, knowledge of individual scores is lost

Question 6

median

Answer 6

the value that lies in the middle of the data when the data set is ordered

Question 7

how to calculate the position of median:

Answer 7

(number of entries+1)/2

• if odd-number=middle of entry
• if even-number=mean of two middle entries

Question 8

pro’s and con’s of median:

Answer 8

pro: little influence by extreme scores, reasonable estimate of what most people mean by the centre of distribution
con: less desirable statistical properties, may not be good to ignore extreme scores in some cases

Question 9

mode

Answer 9

the most frequent value

Question 10

if no entry is repeated…

Answer 10

mode does not exist

Question 11

if two entries occur with the same and highest frequency…

Answer 11

both are modes (biomodal depending on spacing)

Question 12

pro’s and con’s of mode:

Answer 12

pro: the most frequently obtained score, not influenced by extreme scores
con: may not represent a large proportion of all scores, ignores extreme values completely

Question 13

when determining which central tendency value to use, consider:

Answer 13

which central tendency value best represents the bulk of the data, such that there is less confusion between “average” and “mean”

Question 14

order of central tendency values in negative skew:

Answer 14

mean, median, mode

Question 15

order of central tendency values in positive skew:

Answer 15

mode, median, mean

Question 16

if measurement scale is nominal, what is the best indicator of the “middle” usually?

Answer 16

mode

Question 17

if measurement scale is ordinal, what is the best indicator of the “middle” usually?

Answer 17

median (mean is often used since intervals are not equal)

Question 18

if measurement scale is interval, what is the best indicator of the “middle” usually?

Answer 18

mean if symmetrical, median if skewed

Question 19

if measurement scale is ratio, what is the best indicator of the “middle” usually?

Answer 19

mean if symmetrical, median if skewed