2.3/2.4: Variability

Question 1

Central Tendency

Answer 1

Summarizes the most typical values for a variable.

Question 2

What are the measures for central tendency?

Answer 2

1. mean
2. median
3. mode

Question 3

Variability

Answer 3

Describes how spread out the score of a variable are.

Question 4

What are the measures of variability?

Answer 4

• Standard deviation
• Variance
• IQR
• Range

Question 5

If distributions have the same central tendency, do they have the same degrees of variability?

Answer 5

No, they can have different degrees of variability

Question 6

What is the problem with only describing the central tendency of a distribution?

Answer 6

Gives an incomplete description of the data.

Question 7

What are 3 types of data variability?

Answer 7

1. Variability between different subjects
2. Variability within same subjects
3. Measurement error
   - random and systematic

Question 8

Ranges

Answer 8

A measure of variability that indicates how wide the distribution is

Question 9

Absolute Range

Answer 9

Tells us the difference between the smallest and largest observed value.

Question 10

What does range not consider?

Answer 10

Distribution shape

Question 11

What is range highly susceptible to?

Answer 11

Outliers

Question 12

Interquartile Range (IQR)

Answer 12

Indicates the range of the middle 50% of values, between the 25th and 75th percentile.

Question 13

What does IQR tell us about the variables?

Answer 13

What the observations in the middle of the distribution are, without being affected by outliers (skew)

Question 14

What does IQR tell us about the spread?

Answer 14

Where the most commonly occurring values are in a distribution (highest peak)

Question 15

Box and Whisker Plots

Answer 15

Graph the median with IQR and range, which visualizes central tendency and variability together.

Question 16

What make box and whisker plots better for comparing distributions?

Answer 16

When combining them with dot plots

Question 17

How can variability also be conceptualized?

Answer 17

With deviations

Question 18

Deviations

Answer 18

How much each data point deviates from the mean

Question 19

What does it mean when there is a greater deviation of values from the mean?

Answer 19

• Greater spread of scores
  = Greater variability

Question 20

What does a value of 0 in a histogram of deviation mean?

Answer 20

Indicates a score that is the same as the mean of raw scores.

Question 21

Negative Deviation

Answer 21

Most scores are less than the mean

Question 22

Positive Deviation

Answer 22

Most scores are greater than the mean.

Question 23

What should the total negative and positive deviation equal in a normal dstribution?

Answer 23

0

Question 24

How do you quantify the amount of deviation?

Answer 24

1. Find absolute value of all deviation scores
2. Use the Mean Absolute Deviation (M.A.D)

Question 25

Mean Absolute Deviation (M.A.D)

Answer 25

Quantify the mean of the absolute deviation

Question 26

What does a larger MAD score indicate?

Answer 26

Distributions with a greater spread of scores.

Question 27

Taking the mean of the raw deviation scores for a variable gives you: A. sum of squares B. a mean of zero C. the mean absolute deviation D. a measure of the range of the data

Answer 27

Mean of zero - Positive and negative deviations cancel out

Question 28

What is the Sum of Squares?

Answer 28

The sum of the squared standard deviation values.

Question 29

What is the formula for finding the sum of squares?

Answer 29

1. Find the individual score values squared. 2. Add the squared individual score values. 3. Subtract the sum by the (sum of individual scores squared) by the number of scores in the data set.

Question 30

What are the characteristics of population variables?

Answer 30

1. Cannot be measured carefully 2. Predicted with statistics 3. Values are inferred from smaller samples

Question 31

What are the characteristics of sample variables?

Answer 31

1. The sample estimates are what we measure. 2. The values are ideal if the sample estimate is a good estimate of the population. 3. Some adjustments are needed for accurate estimates.

Question 32

What are the symbols used for sample and population mean?

Answer 32

Sample: 𝑋-Bar Population: μ

Question 33

Variance

Answer 33

Gives you an estimate of the average sum of squares

Question 34

How do you find the variance for a population sample?

Answer 34

Divide the sum of squares by the number of data values.

Question 35

What is the result of finding the variance of your population data?

Answer 35

You get the population parameter of variance for your data

Question 36

How do you find the variance of a sample population?

Answer 36

Sum of squares divided by (n-1)

Question 37

What does dividing by (n-1) do to the estimate of sample variance?

Answer 37

It will be higher because you than the population estimate because you are dividing by a smaller number.

Question 38

What is (n-1) also known as?

Answer 38

Degrees of Freedom

Question 39

Degrees of Freedom

Answer 39

The number of values that are truly free to vary in a sample.

Question 40

What sample size will the degrees of freedom have a larger impact on?

Answer 40

Smaller samples

Question 41

How do you find the population standard deviation?

Answer 41

Square the (sum of squares) divided by (total number of data values)

Question 42

How do you find the sample standard deviation?

Answer 42

Square the (sum of squares) divided b (n-1)

Question 43

When are sample standard deviations used?

Answer 43

When you measure from a sample to learn about a larger population

Question 44

When is the population standard deviation used?

Answer 44

If we can measure the true population mean

Question 45

What are the symbols of variance for sample and population?

Answer 45

Sample: s^2 Population: 𝝈^2

Question 46

What are the symbols of standard deviation for sample and population?

Answer 46

Sample: s Population: 𝝈

Question 47

Which measure of variability is in the same units of the original variable? A. sum of squares B. variance C. standard deviation D. sum of squared deviations

Answer 47

Standard Deviation -Squaring the sum of squares makes the values back to normal.