# Central Tendency

What is the function of the measures of central tendency (mean, median, and mode)? Under what circumstances is it most appropriate to use each of the three measures of central tendency? When would three measures of central tendency be beneficial?

“The central tendency of a group of scored refers to the middle of the group of scores” (Aron, Coups, & Aron, 2013, p. 35). There are three measures of central tendency they are: mean, median, and mode. The mean is usually the best measure of central tendency because when calculated properly it gives you the average of a group of numbers. The mean is calculated by adding all of the numbers together and then dividing them by the number of numbers that were added together. Mean would be the most beneficial central tendency to use if you were attempting to calculate the average grade of students in a class. The mode is the most common value in a set of numbers (Aron, Coups, & Aron, 2013, p. 38). It is best to use mode instead of the mean and median if you are attempting to determine which value is the highest or appears the most. Mode would be the most beneficial central tendency to use when conducting a study on what form of public transportation is used the most. The median is the middle number of a set of numbers arranged from smallest to largest. Median would be the most beneficial central tendency to use when attempting to accurately inform people of what type of salary they could earn with a psychology degree. In this case mean would be the best measure of central tendency because it would avoid giving unrealistic expectations of salary based on one or two outliners. If mean was used and a person with a psychology degree became famous and made $5 million then the mean would be much higher than what most people with a psychology degree make. If mode was used then salary would rest at $5 million which is unrealistic for most people.

## Reference

Aron, A., Aron. E., Coups. E. (2014). *Statistics for Psychology* Pearson Education Inc.

2014.

## Hubs to Check

- What is a Median?

The measures of central tendency can help you analyze data. The median is one of these measures along with mode and mean. To learn more about what a median is read on. - Intro to Statistics (for the Social Sciences) #1

I completed my BA in Psychology at the U of O.I am making this page as a way to help me keep these ideas fresh while I am taking a break before I return for a Masters Degree. I hope that this information can help you learn these concepts, too. ...

## Representing Central Tendency in Research

I chose “Transfer high schools: A specific program evaluation for over age high school students” by John Conforti as the quantitative research study for my examination of the methods section and appendices. John Conforti “evaluates the effectiveness of the Good Shepherd transfer high school model in promoting school connectedness and improving graduation rates for over age high school students” (Conforti, 2013). The effectiveness of the Good Shepherd model is examined by looking at graduation rates, student attendance rates, student suspensions, and student responses to the school climate survey in comparison to the performance of traditional high schools without the Good Shepherd model (Conforti, 2013).

The “Transfer high schools: A specific program evaluation for over age high school students” has both a Methodology section and an Appendix A section titled Descriptive Statistics. The Method section is broken into three subsections: participants, procedures, and instruments. The participants section clarifies that the participants of this research study were the student of three New York City Good Shepherd transfer high schools and three traditional New York City public high schools (Conforti, 2013). The procedure section explains the reasons that each high school was considered eligible for the study and the parameters each school had to fit. The instruments section describes the types of data that were collected and used to judge the effectiveness of the Good Shepherd transfer high schools in comparison to tradition schools. Appendix A: Descriptive Statistics has multiple tables of data that show the quantitative data that came from the different instruments used during the research study such as: “School Climate Survey Results Transfer and Traditional High Schools”, “Mean Attendance and Suspension Rates for Transfer and Traditional High Schools”, and “Mean Graduation and Dropout Rates for Traditional and Transfer High Schools” (Conforti, 2013).

For the purpose of this research study John Conforti used the central tendency known as mean. The mean is an “arithmetic average of a group of scores” (Aron, Coups, & Aron, 2013, p. 35). The mean was used to represent the attendance rate, graduation and dropout rate, and the result of the climate survey from the Good Shepherd transfer high schools to tradition high schools. John Conforti was then able to compare the mean of the data from each category in order to determine which type of high school proved the most effective in attendance, graduation, and student satisfaction.

## Refrences

Aron, A., Aron. E., Coups. E. (2014). *Statistics for Psychology* Pearson Education Inc. 2014.

Conforti, J. (2013). *Transfer high schools: A specific program evaluation for over age high **school students. *(Order No. 3570533, Fairleigh Dickinson University). *ProQuest Dissertations and Theses, *, 71. Retrieved from http://ezproxy.snhu.edu/login? url=http://search.proquest.com/docview/1420308054?accountid=3783. (1420308054).

## Chapter 3: Some Key Ingredients for Inferential Statistics: Z Scores, the Normal Curve, Sample versus Population, and Probability

*Z* Scores

Number of standard deviations a score is above or below the mean

Formula to change a raw score to a *Z *score:

*Z* Scores

Formula to change a *Z* score to a raw score:

Distribution of *Z* scores

Mean = 0

Standard deviation = 1

The Normal Distribution

Normal curve

The Normal Distribution

Normal curve and percentage of scores between the mean and 1 and 2 standard deviations from the mean

The Normal Distribution

The normal curve table and *Z* scores

Shows the precise percentage of scores between the mean (*Z* score of 0) and any other *Z* score

Table also includes the precise percentage of scores in the tail of the distribution for any *Z* score

Table lists positive *Z* scores

The Normal Distribution

Steps for figuring percentage area above

or below particular raw or *Z *score:

Convert raw score to *Z *score (if necessary)

Draw normal curve, locate where *Z* score

falls on it, and shade in area for which

finding percentage

3. Make rough estimate of shaded area’s percentage (using 50%-34%-14% rule)

The Normal Distribution

Steps for figuring percentage area above or

below particular raw or *Z *score:

4. Find exact percentage using normal curve table

5. If needed, add or subtract 50% from this percentage

6. Check that exact percentage is within range of estimate from Step 3

The Normal Distribution

Steps for figuring *Z* scores and raw scores

from percentages:

Draw normal curve, shade in approximate area for the percentage (using the 50%-34%-14% rule)

Make rough estimate of *Z* score where shaded area stops

Find exact *Z* score using normal curve table

The Normal Distribution

Steps for figuring *Z* scores and raw scores

from percentages:

Check that *Z* score similar to rough

estimate from Step 2

To find a raw score, change it from *Z*

score

Sample and Population

Population

Sample

Methods of sampling

Random selection

Haphazard selection

Sample and Population

Population parameters and sample statistics

Probability

Probability

Expected relative frequency of a particular outcome

Outcome

The result of an experiment

Probability

Range of probabilities

Proportion: from 0 to 1

Percentages: from 0% to 100%

Probabilities as symbols

*p*

*p < .05*

Probability and the normal distribution

Normal distribution as a probability distribution

Controversies and Limitations

Is the normal curve really so normal?

What does probability really mean?

Sample and population