Ch. 3 : Numerical Summaries of Center and Variation

Question 1

What to use when measuring Center?

Answer 1

To measure the “typical value” use: mean, median, mode

Question 2

Mean

Answer 2

Add all data and divide by number of observations

Question 3

Median

Answer 3

the midpoint of ranked values (from small to large)

• if have even observations, take two in middle and take average (that is new median)
• resistant to outliers

Question 4

Mean vs Median

Answer 4

Symmetric: mean=median
Skewed: center is the median
(right: median<median)

Question 5

What to use when measuring Spread?

Answer 5

Measured by: Standard Deviation, IQR, and Range

Question 6

Standard Deviation

Answer 6

described by the square root of the variance
(The avg distance of a value from the mean)
-it represents a typical distance from the mean of observations
–deviation: take each data point , subtract the mean, and then square that difference

Question 7

Finding IQR

Answer 7

Q3-Q1= iqr (the middle 50% of the data)

Question 8

Range

Answer 8

Max-MIn

-poor measure of spread

Question 9

Which Center and Spread are best?

Answer 9

Use Mean & Standard Deviation when distribution symmetric/unimodal
Use Median & IQR when distribution is skewed L or R

Question 10

Review for Center

Answer 10

Use Mean for typical value of symmetric

Median for typical value of skewed

Question 11

Review for Spread

Answer 11

Use SD for symmetric

Use IQR for skewed

Question 12

Empirical Rule

Answer 12

rough guideline that helps understand how SD measures variability (68% to 95% to 99.7%)