Descriptive Statistics

A Short Course in Statistics

Descriptive Statistics

Consists of the collection, organization, summarization, and presentation of data.

Often with charts and graphs. 0

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Collecting Data

If you can collect data from everyone or everything in your target of interest you have a POPULATION.

The population is the whole entire group of interest

Collecting Data

Usually it is IMPOSSIBLE to collect every piece of data. In this case you have to use a SAMPLE.

The sample is just part of the whole group of interest

After Collecting the Data

Now it is time to do some calculations and make some graphs!We will start with determining some basic measures of central tendency.Measures of central tendency measure the center of data.We will learn to determine Mean, Median and Mode

Mean

When you usually think of a "middle" score they often think of what is known as the arithmetic mean or just mean, for short.

This is what most people also refer to as the "average" of a set of scores.

I call the Mean the mathematical middle.

You probably already know how to calculate the mean for a simple list of numbers.

Add all the numbers and then divide by the number of numbers you have, remember doing this before?

Let’s Calculate the MeanThe following is a list of Elliott’s test score from his math course.

Test 1 68Test 2 72Test 3 90Test 4 86

Now add the numbers together68+72+90+86 = 316

Now divide 316 by 4 (the number of numbers) = 79

79 is the Mean for Elliott’s Math Scores

Try Your Own Problem #1

Matt’s test scores are as follows:

Test 1 90Test 2 88Test 3 97Test 4 80Test 5 70

What was the Mean of Matt’s test scores?

Let’s take a look.

Median The median is the number at which half your data pieces are more than that number and half are less than that number. The median cuts the data set in half.

To calculate the mean the data list must be in numerical order, either smallest to largest or largest to smallest.Generally, the median provides a better measure of location than the mean when there are some extremely large or small observations that skew the data. For this reason, median income is used as the measure of location for the U.S. household's income.

Let’s Find the Median

The following list is the attendance in my classes on Tuesday

23, 20,16, 30, 8

First put the list in numerical order.

8, 16, 20, 23, 30

Position of the median can be determined by using the formula

Look for the number that is in the 3rd position.The 20 is the Median of this data set.

Try your own problem #2

Data List23, 24, 3, 26, 2, 9, 13, 6

Ordered List 2, 3, 6, 9, 13, 23, 24, 26

Find the position(8+1)/2= 4.5th

Look for the 4.5th number.Since the 4.5th does not exist, find the 4th and the 5th and find the mean of the two numbers.What’s the Median?

Let’s Take a Look!

2

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Mode

The mode is the most "typical" value The Mode it is the most repeated value in the data set. There might be no mode in a data set, this happens when all numbers only appear once .There may be more than one mode, this happens when more than one data value appears many times. If there is more than one mode, all values must appear in the list the same number of times.The Mode is most frequently used when describing qualitative data like religious preference or eye color.

Let’s Determine the Mode

Your data list does not need to be in order, but ordering the list might make it easier to find the Mode.

2,2,3,5,6,7,7,7,8,9Which number occurs the most often in this list?The 7, so 7 is the Mode of this set.

2,2,2,3,4,5,7,7,7,8,9This list has two modes, both the 2 and the 7 are the modes.

Try your own problem #3

2, 5, 7, 8, 7, 6, 9, 4, 6, 8, 2, 3, 1, 4, 5, 6

Start by ordering the list(Just to help you out a little)

1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9

Which data value appears the most?

Let’s Take a Look!

End of the Lesson

You have reached the end of our first lesson on descriptive statistics.You should be able to figure mean, median and mode for an ungrouped list of data.Stop in again for a second lesson, Making Graphs with Data, coming soon.Thanks, Cindy

Answers for Try Your Own Problems

#1 Matt’s Mean is 85. Return to lesson

#2 The Median is 11. Return to lesson

#3 The Mode is 6. Return to lesson