4_Variability

# 4_Variability - Descriptive Statistics Measures of...

This preview shows pages 1–14. Sign up to view the full content.

Descriptive Statistics Measures of Variability You should be able to . . . • Define and compute the: – Range – Variance • Parameter and statistic – Standard deviation • Parameter and statistic • Define and explain bias

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
• We have discussed measures of central tendency • Now we need measures to describe the degree to which observations: cluster together or differ or deviate
Measures of Variability • Measures that indicate the degree of difference among observations Range • A measure of variability that is the distance from the lowest score to the highest score • Range = (highest X - lowest X) + 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example Distribution • What is the range? 230 200 200 150 140 130 130 130 100 80 Example Distribution • What is the range? 230 200 200 150 140 130 130 130 100 80
Example Distribution • What is the range? • (230 - 80) + 1 = 151 230 200 200 150 140 130 130 130 100 80 Range

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problems with the range • Based on only two observations • As number of observations increases, range increases WHY? • There is an increased probability of extreme values 44 46 42
44 50 46 58 43 42 40 Interquartile Range • Range for the middle 50% of the observations – Chop off top 25% of observations – Chop off bottom 25% of observation

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Interquartile Range Procedure for determining IQR • 1. Order observations from least to most • 2. Find positions in the distribution that divide observations into quarters – (number of observations +1) / 4 • Now we can remove the top and bottom quarters
Procedure for determining IQR • 3. Count from the bottom up for first quartile • 4. Count from the top down for third quartile • 5. IQR = number at top of third quartile - number at top of first quartile Example Distribution • What is the IQR? 230 200 200 150 140 130 130 130 100 80

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example Distribution • What is the IQR? • (10+1)/4 2.75 230 200 200 150 140 130 130 130 100 80 Example Distribution • What is the IQR? • (10+1)/4 2.75 230 200 200 150 140 130 130 130 100 80 The position between the 2 nd and 3 rd scores
Example Distribution • What is the IQR? • (10+1)/4 2.75 230 200 200 150 140 130 130 130 100 80 The position between the 2 nd and 3 rd scores Example Distribution • What is the IQR? • (10+1)/4 2.75 230 200 200 150 140 130 130 130 100 80 200 115

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example Distribution • What is the IQR? • (10+1)/4 2.75 • 200 - 115 = 85 230 200 200 150 140 130 130 130 100 80 200 115 Advantage of IQR over range: • Not sensitive to extreme values
• Range and IQR define variability based on two values • We could also describe variability by describing how much each

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 63

4_Variability - Descriptive Statistics Measures of...

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online