EXAM TOMORROW

Aim: Review for Exam

Properties of Standard deviation

SD measures the spread about the mean and should be used only when the mean is chosen as the measure of center.

The larger the standard deviation, the more disperse, or spread out, the distribution is.

Summary of the Properties of the Theoretical Normal Distribution

Normal Distribution: is a continuous, symmetric, bell shaped distribution of a variable.

The mean, median and mode are equal and located at the center of the distribution.

Curve never touches the x-axis but gets increasingly closer.

Population variance and Standard deviation

Population Variance/Standard Deviation - measures the variability of data in a population

VARIANCE STANDARD DEVIATION

2i

X

x x

n

22 i

X

x x

n

Sample Variance and Standard Deviation

Sample Variance/Standard Deviation- measures the variability of data in a sample- Usually based on a small and manageable sample size

VARIANCE STANDARD DEVIATION 2

1

ix xS

n

22

1

ix xS

n

Different Distributions

Bimodal Distribution

J-Curve

Group Frequency Distribution

Procedure: 1.Find class limits:

1. Find range of data2. Find the width (range divided by number of classes)

always an odd number

2.Find class boundaries: (one decimal place more)1. Add 0.5 to upper class limit2. Subtract 0.5 to lower class limit

3.Fill in tally, frequency and cumulative frequency

Example

Class Limit

Class Boundaries

Tally Frequency

Cumulative Frequency

100-104

99.5-104.5 // 2 2

105-109

104.5-109.5 //// /// 8 10

110-114

109.5-114.5 //// //// //// ///

18 28

115-119

114.5-119.5 //// //// ///

13 41

120-124

119.5-124.5 //// // 7 48

125-129

124.5-129.5 / 1 49

130-134

129.5-134.5 / 1 50

Finding the Class Midpoint

Class Midpoint: obtained by adding the lower and upper

boundaries and dividing by 2

OR adding the lower and upper limits and dividing

by 2.

mX

mX Lower limit + Upper limit 2

Lower boundary + Upper boundary 2

Finding Outliers

1. Find the first quartile and third quartiles2. Find the IQR (third quartile – first quartile)3. Multiply IQR by 1.54. Find Boundaries

1. First Quartile – Step 32. Third Quartile – Step 3

5. Any data below Step 4-1 or above Step 4-2 are outliers

EXAM TOMORROW

Aim: Review for Exam

Review Sheet Question #1

Class Limit

Class Boundaries

Tally Frequency Cumulative Frequency

Review Sheet Question #2

Find the range, variance and standard deviation of the following data. Assume that the data represents a sample of the population.

32, 36, 46, 20, 32, 18, 16, 34, 26, 27, 26

Review Sheet Question #3

Check the data for outliers: 14, 18, 27, 26, 19, 13, 5, 25

Review Sheet Question #4

A dietitian is interested in comparing the sodium content of real cheese with the sodium content of a cheese substitute. The data for two random samples are shown. Compare the distributions, using boxplots.

Real Cheese 310, 420, 45, 40, 220, 240, 180, 90

Cheese Substitutes 270, 180, 250, 290, 130, 260, 340 310

Review Question #5

a. What is incorrect about the construction of the frequency distribution below?

b. Find the midpoint of the first class below using the midpoint formula:

Class Frequency27-32 133-38 039-44 645-49 450-55 2