Module 4: Variability

Question 1

What is Variability?

Answer 1

Refers to how different, scattered or spread the scores/data are

Question 2

How do we describe a data distribution’s variability?

Answer 2

• Standard Deviation
• Density Plot

Question 3

What are 4 Measures of Variability?

Answer 3

• Range
• Interquartile Range
• Variance
• Standard Deviation

Question 4

What is the Range?

Answer 4

The difference b/w the highest and lowest scores

Range = Maxmimum - Minimium

Range = 142 - 60 = 82 kg

must include units

Question 5

How is Range Reported?

Answer 5

Cant report the range alone
must report the max and min along with the range

Ex. The bench press 1RM minimum and maximum scores were 60 and 142 kg with a range of 82 kg

If we reported just the range, 82 kg could come from any max/min such as 100-182 or 10-92

Question 6

What are the Strengths and Limitations of using Range?

Answer 6

Strength
- Easy to Compute
- Gives sense of values in the variable (when max/min included)

Limatations
- Affected by Outliers
- It may not show the variability within the distribution
- Not useful for hypothesis Testing based on distributions

Question 7

What is the Interquartile Range? (IQR)

Answer 7

Difference between the 25th and 75th percentile

AKA: IQR = Q3 - Q1

Ex.

Question 8

How do we report IQR?

Answer 8

• The bench press 1RM Q1 and Q3 scores were 93 and 128 kg with an IQR of 35 kg.

OR

• The bench press 1RM 25th percentile and 75th percentile scores were 93 and 128 kg with an IQR of 35 kg.

Question 9

What are the Strengths and Limatations of using IQR?

Answer 9

Strengths
- Not affected by Outliers

Limatations
- Ignores 50% of the data (upper 25% and lower 25%)
- Not useful for hypothesis testing based on distributions

Question 10

What is Variance?

Answer 10

The avereaged squared deviation from the mean

Question 11

How do we calculate Variance?

Use this Data Set

Answer 11

Step1: Find the Mean = 106
Step 2: Calculate the Differnces and Scores

Step 3: Take the Sum of Squared Differences and divide by N-1

Question 12

What is the Computational Formula for calculating Variance?

Answer 12

Question 13

How do we report Variance?

Answer 13

The bench press 1RM variance was 575.4

/

The weight variance was 1938.6

no units

Question 14

What are the Strengths and Limatations of using Variance?

Answer 14

Strengths
- Calculated from all the scores in the distribution
- useful for hypothesis based on distributions

Limitations
- Affected by Outliers
- Not directly interpretable (no unit of measurment)

Question 15

What is Standard Deviation?

Answer 15

Question 16

What are the Strengths and Limitations of using Standard Deviation?

Answer 16

Strengths
- Calculated from all the scores in the distribution
- useful for hypothesis based on distributions
- Directly Interpretable (units of measurement)

Limitations
- Affected by Outliers

Question 17

How do the symbols of Variance and Standard Deviation differ in populations and samples?

Answer 17

Question 18

What measures of central tendency and measure of variabilities are usually reported together?

Answer 18

Question 19

What statistics are reported in symmetrical distributions?

Answer 19

Symmetrical distributions

• The mean of the weight was 198.2 lbs with a standard
  deviation of 44.0 lbs
• The weight has a mean and SD of 198.2 ± 44.0 lbs

Question 20

What statistics are reported in asymmetrical distributions?

Answer 20

Asymmetrical distributions

• The median weight was 186.0 lbs, with the 25th and 75th
  percentiles of 168.0 and 222.0 lbs, respectively (IQR =
  54.0 lbs).
• The median weight and its corresponding Q1 and Q3
  were 186.0 lbs (168.0, 220.0; IQR = 54.0)