Part IISigma Freud and

Descriptive Statistics

Chapter 2

Computing and Understanding Averages:Means to an End

Objectives

• Measures of central tendency• Computing the mean using AVERAGE (function)• Computing the mode using MODE (function)• Computing the median using MEDIAN (function)• Computing descriptive statistics using the

Analysis ToolPak• Selecting a measure of central tendency

Measures of Central Tendency

• AVERAGE - “Measures of Central Tendency”– A single score representing a set of scores

• Major types – Mean – typical average score– Median – middle score– Mode – most common score

Computing the Mean

• Formula for the mean

• “X bar” is the mean value of the group of scores • “” (sigma) tells you to add whatever follows it• X is each individual score in the group• n is the sample size

The Mean in three Easy Steps

• List the entire set of values in one or more columns. These are all the X’s.

• Compute the sum or total of all values• Divide the total or sum by the number of

values

– The answer you get is the Mean

Location Number of Annual Customers

Lanham Park store 2,150

Williamsburg store 1,534

Downtown store 3,564

Mean Example

Using the AVERAGE Function

• Select the cell for the AVERAGE function• Create a formula to average the three values

– =(A1+A2+A3)/3• OR type the AVERAGE function

– =AVERAGE(A1:A3)

More Excel

• Arithmetic Mean– Sum of the deviation is equal to zero

• Geometric Mean– GEOMEAN uses multiplication instead of addition

• Moving Mean– More accurate…good for unique distributions

• Weighted Mean– Accounts for the frequency of a score’s occurrence

Things to Remember

• A small n represents the sample size.• A large N represents the population size.• The sample mean is the central tendency

measure that most accurately reflects the population mean.

More Things to Remember

• The mean is like the fulcrum on a seesaw. – The centermost point is where all the values on

one side of the mean are equal to all the values on the other side of the mean.

• The mean is very sensitive to extreme scores.– Extreme scores can pull the mean in one direction

or another and make it less representative of the set of scores.

Weighted Mean Example

Weighted Mean Example

Computing the Median

• Median = score at which 50% of scores fall above and 50% fall below

• No standard formula– Rank order scores from highest to lowest or

lowest to highest– Find the “middle” score

• BUT…– What if there are two middle scores?– What if the two middle scores are the same?

Using the MEDIAN Function

– Select the cell and type the MEDIAN function– =MEDIAN(A2:A7)

Things to Remember

• The Median is the middle point of a set of cases.

• Since the Median uses the number of cases, not the values of those cases, extreme scores (outliers) do not influence the Median.

Do it

• What does it mean if the Mean and Median are about the same?

• What does it mean if the mean and Median are very different?

Computing the Mode

• Mode = most frequently occurring score• No formula

– List all values in the distribution– Tally the number of times each value occurs– The value occurring the most is the mode– Democrats = 90– Republicans = 70– Independents = 140 – the MODE!!

– When two values occur the same number of times -- Bimodal distribution

Using the MODE.SNGL Function

Using the MODE.MULT Function

Do it

• Describe– 2 cases where the Mean is best– 2 cases where the Median is best– 2 cases where the mode is best

Descriptive Statistics ToolPak

Descriptive Statistics ToolPak

Make It Pretty

How to Make it Pretty

• Format entire worksheet in Arial 12,• Format numbers so they make sense.• Deleted the Mode cells (there is no mode).• Used Format > Column > AutoFit to adjust the

columns.• Could have used:

– Color– Table formats– Shading

Always start by getting acquainted with the data.Simply describe it.

Summary