Ch 4 Variability

Range formula for a continuous variable

Range = URL for X(max) - LRL for X(min)

Range formula (for variables w/ precisely defined upper and lower boundaries)

Range = X(max) - X(min)

Range formula (when scores are whole #s)

Range = X(max) - X(min) +1

How many scores in the distribution are used to compute the range? a. only 1 b. 2 c. 50% of them d. all of the scores

B

Standard deviation is probably the most commonly used value to describe and mea- sure variability. Which of the following accurately describes the concept of standard deviation? a. the average distance between one score and another b. the average distance between a score and the mean c. the total distance from the smallest score to the largest score d. one half of the total distance from the smallest score to the largest score

B

What is the value of SS, the sum of the squared deviations, for the following population of N = 4 scores? Scores: 1, 4, 6, 1 a. 0 b. 18 c. 54 d. 122² = 144

B

A population has a mean of m = 35 and a standard deviation of s = 5. After 3 points are added to every score in the population, what are the new values for the mean and standard deviation? a. m=35 and s=5 b. m=35 and s=8 c. m=38 and s=5 d. m=38 and s=8

C

What is the range for the following set of scores? 3, 7, 9, 10, 12 a. 3 points b. 4 or 5 points c. 9 or 10 points d. 12 points

C

Variance (σ²)

the mean of the squared deviations; the average squared distance from the mean SS/N = Σ(X - μ)²/n

t/f Adding a constant value to every score in a distribution does not change the standard deviation. Multi- plying every score by a constant, however, causes the standard deviation to be multiplied by the same constant.

true

A sample statistic is ____________ if the average value of the statistic is equal to the population parameter.

unbiased

formula for adjusted sample variance

*using n-1 for sample variance produces an unbiased statistic

The calculation of variance and standard deviation

1. determine the deviation score (X - μ) 2. calculate the mean of deviation scores Σ(X - μ)(should be 0) 3. compute variance; gets rid of the ± signs Σ(X - μ)²/n 4. find standard deviation = √variance

What is the variance for the following set of scores? 2, 2, 2, 2, 2 a. 0 b. 2 c. 4 d. 5

A

Which of the following sets of scores has the greatest variability? a. 2,3,7,12 b. 13, 15, 16, 17 c. 24, 25, 26, 27 d. 42, 44, 45, 46

A

How is the standard deviation represented in a frequency distribution graph? a. By a vertical line located at a distance of one standard deviation above the mean. b. By two vertical lines located one standard deviation above the mean and one standard deviation below the mean. c. By a horizontal line or arrow extending from a location one standard deviation above the mean to a location one standard deviation below the mean. d. By a horizontal line or arrow extending from the mean for a distance equal to one standard deviation.

D

What is the standard deviation for the following population of scores? Scores: 1, 3, 7, 4, 5 a. 20 b. 5 c. 4 d. 2

D

Variability

a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together

a sample statistic is said to be _______________ if, on the average, it consistently overestimates or underestimates the corresponding population parameter

biased

purpose of variability

describe the distribution, measure how well an individual score represents the distribution

deviation

distance from the mean deviation score = X - μ

t/f samples tend to be more variable than populations

false

standard deviation σ

is the square root of the variance and provides a measure of the standard, or average distance from the mean.

What is the problem with using the range as a measure of variability?

it is completely determined by the two extreme values and ignores the other scores in the distribution. Thus, a distribution with one unusually large (or small) score will have a large range even if the other scores are all clustered close together.

What are the 3 measures of variability?

range, variance, standard deviation