Chapter 2 ~ Describing Location in a Distrubtion

Question 1

Z-score

Answer 1

Compares individual data points to the mean of the set of data by measuring how far these points lie from the mean (using standard deviations as the unit).
(X – μ)/σ

Question 2

What is the sample mean of the z-scores?

Answer 2

0

Question 3

What is the sample standard deviation of the z-scores?

Answer 3

1

Question 4

Density curve

Answer 4

A curve that always lies on or above the horizontal axis and has an area of exactly 1 underneath it. It approximates the shape of an actual distribution.

Question 4

Median of a density curve

Answer 4

Divides the area under the curve in half. Never directly at the peak unless the distribution is symmetrical.

Question 5

Mean of a density curve

Answer 5

The point at which the curve would balance if it was made of solid material. Pulled towards the tail if the distribution is skewed.

Question 6

Normal curve

Answer 6

Most commonly used family of density curves.
Symmetric, bell shaped, unimodal.
Mean and standard deviation determine the centre and spread of the curve.

Question 7

Empirical Rule

Answer 7

a.k.a. The 68–95–99.7 Rule
In a normal distribution with mean μ and standard deviation σ,
68% of the observations fall within 1σ of μ
95% of the observations fall within 2σ of μ
99.7% of the observations fall within 3σ of μ

Question 8

Standard Normal Distribution

Answer 8

A normal distribution with mean 0 and standard deviation 1

Question 9

What is the symbol notation for expressing normal distributions?

Answer 9

N(μ, σ)

Question 10

The area under a normal curve between two given values is the same as _________________________.

Answer 10

The area us we the standard normal curve between their z-scores