Chapter 4

Question 1

measure of central tendency

Answer 1

• tells us what sample is like on average

- mean, median, mode

Question 2

2 stats needed to describe data

Answer 2

• measures of central tendency

- measures of variability

Question 3

mode

Answer 3

• most frequent score
• appropriate with nominal, ordinal, interval, or ratio data
• easily found from ungrouped frequency distribution
• symbol: Mo

Question 4

median

Answer 4

• score that divides group in half (50% fall below, 50% fall above -> that’s why it’s aka P50)
• appropriate with ordinal, interval, or ratio data
• to find: rank-order scores from highest to lowest
• if number of scores is even, median is midpoint between 2 middle scores
• symbol: Mdn

Question 5

mean

Answer 5

• adding all scores and dividing by number of scores
• can only be used with interval or ratio data
• symbol: mu (Greek letter u)

Question 6

symbols: X, X bar, sigma, ux (mu subscript x), N, n

Answer 6

• X: number of scores in pop.
• X bar: mean of a sample of scores
• sigma: Greek E, means add up whatever comes after it
• ux: the mean of a population of scores
• N: population size
• n: sample size

Question 7

deviation score

Answer 7

• X-X bar
• shows how much the score differs from the mean
• should add up to 0 if you do this for all scores in the distribution

Question 8

outlier

Answer 8

• extreme score in the distribution

- median is less sensitive than the mean is to outliers

Question 9

open-ended distributions

Answer 9

• when exact scores cannot be recorded at one end of the distribution
• ex. bystander experiment: when nobody helped and the confederate had to stand up to avoid being trampled -> we can’t calculate mean time without assuming how long it would have taken someone to help

Question 10

score transformations and central tendency

Answer 10

• process that changes every score in a distribution to one on a specific scale (ex. scaling)
• ex. if we add (or subtract) 10 points to all scores, the mean of all scores will increase (or decrease) by 10 points
• ex. if we multiply (or divide) all scores by 2, the mean of all scores will become twice as large (or small)
• these are all linear transformations as they preserve the linear relationship between original and transformed scores

Question 11

central tendency and skewed disributions

Answer 11

• in symmetrical distributions with 1 mode (ex. normal curve), Mu, Md, Mo have same value
• in skewed distributions, mean is pulled towards extreme scores at tail, and median gets pulled about 2/3rds of the way to extreme (between Mu and Mo)

Question 12

which measure of central tendency satisfies the least squares criterion?

Answer 12

the mean

Question 13

which measure of central tendency is best?

Answer 13

• Mode is preferred for categorical variables
• Median is preferred for descriptive purposes
• Sample mean is preferred for inferential purposes (more reliable)