Chapter 3 Variability

What is the standard deviation of these data?

2.08

The variance (σ2) is the:

typical squared deviation from the mean.

When using a sample to estimate a population's variability the SS is divided by N − 1 rather than N to correct for a sample's tendency to:

underestimate the variability of a population.

What symbol represents the standard deviation of a population?

σ

Which equation defines the sum of the squared deviation scores? a.∑(𝑋−𝜇)2∑(X−μ)2 b. ∑(𝑋−𝜇)∑(X−μ) c. 𝜎2‾‾‾√σ2

A

What characteristic of a distribution of scores does a standard deviation describe?

All of the above

Why is the range a poor measure of variability?

It uses only two values rather than all of the values in the distribution.

What measure of variability should be used when the data are ordinal?

Range

What symbol represents the standard deviation of a sample?

SD

SPSS can only be used to compute the standard deviation of a sample, not a population.

True

The SS is computed in exactly the same way for a sample and a population.

True

Statisticians square each derivation score so that:

a. when they sum them they will not sum to zero.

When computing the variance of an entire population, you are performing _____________ so divide the SS by ___.

descriptive statistics, N

When you are using a sample to estimate a population's standard deviation you are doing ________ statistics.

inferential

When estimating the variance of a population from a sample, you are performing _____________ so divide the SS by _____.

inferential statistics, N - 1

When computing a sample's standard deviation there _________ to the computation process relative to when you are computing a population's standard deviation.

is one change

SS stands for the:

sum of the squared deviation scores.

The smallest standard deviation that is possible is ____ because this would mean that ______.

0; all of the scores are the same

Which equation is used for computing the SS? a. b. 𝑆𝑆=∑𝑋2−(∑𝑋)2𝑁SS=∑X2−(∑X)2N c.

B

The definitional method for finding the SS and the computational method for finding the SS will ALWAYS provide the same value but in most situations the __________ method is faster and will not produce any rounding error. Definitional Method, 𝑆𝑆=∑(𝑋−𝜇)2SS=∑(X−μ)2 Computational method,𝑆𝑆=∑𝑋2−(∑𝑋)2𝑛SS=∑X2−(∑X)2n

Computational method

In order for two data sets to have the same standard deviation, they must have the same mean

False

A deviation score measures:

the distance of an individual score from the mean.

The standard deviation (σ) is:

the typical distance of all the scores from the mean, some scores will be further away and some closer but this is the typical distance.