Chapter 4-Variability: Lecture

Question 1

variability

Answer 1

• refers to how much scores in a dataset differ from each other
• how the scores are scattered around the central point
• the concept of spread in the data

Question 2

Why measure variability?

Answer 2

• It describes the data set’s distribution (clustered vs. spread out)

Question 3

How can variability be measured?

Answer 3

• with the range
• with the variance/standard deviation

in both cases, variability measures distance

Question 4

Range v1

Answer 4

highest score - lowest score

dataset: 3,7,8,9 range= 6

Question 5

Range v2

Answer 5

lowest score and highest score (ex. 3 to 9)

Question 6

range limitations

Answer 6

• range is useful as a very rough approximation of variability (ex. scores on an exam)
• But, it is an imprecise and unreliable measure of variability, as it is based on two scores (not all)

Question 7

When using the man what do we compute to describe variability in the data?

Answer 7

• the variance and standard deviation

Question 8

Variance definition

Answer 8

the average squared deviation from the mean
-raw way to measure variability

Question 9

Standard deviation

Answer 9

• the most common measure of variability
• measures the average distance from the mean for scores in a dataset
• variance determines standard deviation
• useful way to measure variability

Question 10

Sum of squares

Answer 10

the sum of the squared deviations

Question 11

variance

Answer 11

the average of the squared deviations

Question 12

standard deviation

Answer 12

the square root of the variance

Question 13

Standard deviation self- check

Answer 13

• the SD can never be less than the distance between the mean and the least deviant score
• the SD can never be greater than the distance between the mean and the most deviant score

Question 14

notes about n-1

Answer 14

• for samples we divide by the n-1 when calculating the variabce to inflate the variance estimate
• n-1 is the degrees of freedom (df) for S
• accounts for the fact that sample variance will typically underestmate population variance
• the effect is stronger with smaller samples and the effect of df helps account for that too

Question 15

What happens if a constant is added or subtracted to every score?

Answer 15

• the standard deviation will not be changed
• the spread/variability does not change

Question 16

What happens if a constant is divided or multipled to every score?

Answer 16

• the SD will be multiplied or divided by the same constant
• it will multiply the distance between scores, and the sd measures this distance

Question 17

mean and SD as descriptive statistics

Answer 17

• mean and sd do a good job of describing most distributions, particulary if there isnt too much skew
• if given mean and standard deviation you can construct a rough sketch of the distribution