Central Tendancies

· Central Tendency, Variability, Normal Curve, Z Score

Overview

Answer questions related to central tendency, variability, normal curve, z score, probability, and binomial distribution.

By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and assessment criteria:

Context

When data are collected as part of the research process, the scores have some sort of manner in which they fall. Central tendency talks about the center of the distribution, while variability discusses the spread of scores within the distribution. The scores can be converted to standard scores to increase the understanding among researchers, as well as to further describe how they fall within the distribution.

Scores can be converted to standard scores to increase the understanding among and between researchers as well as to further describe how these scores fall within the distribution. You will further explore this with z scores.

Many statistical analyses use an assumption that data falls in a normal distribution. It is important to understand the normal curve as well as the area under the curve as it relates to standard scores. Probability examines the likelihood of an event occurring.

· Toggle Drawer

Questions to Consider

To deepen your understanding, you are encouraged to consider the questions below and discuss them with a fellow learner, a work associate, an interested friend, or a member of the business community.

Central Tendency and Variability in the Real World

. Why does scale of measurement matter in determination of which measures of central tendency and variability are appropriate?

The Normal Curve

. Pick a continuous variable (that is, interval or ratio in scale of measurement) that is normally distributed. Analyze the distribution of the variable. What do scores in the center of the distribution mean for this particular variable? What about scores in the tails?

. Imagine you have a z score of +2.58. What does that mean in terms of your specific variable?

Resources

Required Resources

The following resources are required to complete the assessment.

Capella Resources

Click the links provided to view the following resources:

. assessment2a.sav .

. assessment2b.sav .

. Probability Binomial Table .

. Area Under Normal Curve Table .

SPSS Software

You are required to have the following software to complete your assessments throughout the course:

. SPSS Statistics Premium Campus Edition, Base GradPack or Standard GradPack (version 22 for Windows or Mac).

Note: Versioning: This software is routinely updated. While version 22 of the IBM SPSS Statistics is recommended, older versions may be used if you already own or have access to them for the duration of this course. Arrange the required statistical software for your operating system (PC or Macintosh).

If you have access to statistical software such as SAS or Excel with the appropriate add-in such as XLSTAT, you may use these as long as they meet the requirements of this course.

As a learner, you may purchase this software at a substantially reduced price from the  bookstore . Read the descriptions carefully to make sure you buy the correct software for your operating platform (PC or Macintosh) and course needs.

Suggested Resources

The following optional resources are provided to support you in completing the assessment or to provide a helpful context. For additional resources, refer to the Research Resources and Supplemental Resources in the left navigation menu of your courseroom.

Multimedia

Click the links provided below to view the following multimedia pieces:

. Modules: 5 and 6  |  Transcript .

. Module 5. Mode, Median, and Mode.

. Module 6. Range, Variance, and Standard Deviation.

· Modules: 7, 8, 10, and 11  |  Transcript .

. Module 7. Percent Area and the Normal Curve.

. Module 8. z Scores.

. Module 10. Probability Definitions and Theorems.

. Module 11. The Binomial Distribution.

· Central Tendency and Variability  |  Transcript .

· z Score Calculation  |  Transcript .

. You may wish to review this presentation for an example of calculating a z score. You might take note of the use of the normal curve, how z scores fall along the normal curve, and how we utilize different portions of the normal curve in our calculations.

Course Library Guide

The University library guide has been created specifically for your use in this course. You are encouraged to refer to the resources in the  PSYC-FP4700 – Statistics for the Behavior Sciences Library Guide  to help direct your research.

Internet Resources

Access the following resources by clicking the links provided. Please note that URLs change frequently. Permissions for the following links have been either granted or deemed appropriate for educational use at the time of course publication.

· Shodor Education Foundation. (2013).  Interactivate: Probability and outcome . Retrieved from http://www.shodor.org/interactivate/discussions/ProbabilityAndOutcom/

· Sophia Learning . (2014). Retrieved from http://www.sophia.org

. Capella University partners with Sophia Learning to provide tutorials and other learning resources online.

· StatisticsLectures.com . (2012). Retrieved from http://statisticslectures.com/

. This Web site offers resources that cover many topics in statistics, including presentations that illustrate how to use software to implement statistical methods.

· Khan Academy . (2013). Retrieved from https://www.khanacademy.org

. This Web site offers resources covering a range of subjects, including statistics.

· Stat Trek . (2014). Retrieved from http://stattrek.com/

· Stat Soft: Electronic Statistics Textbook . (2014). Retrieved from http://www.statsoft.com/Textbook

Bookstore Resources

The resources listed below are relevant to the topics and assessments in this course and are not required.

Steinberg, W. J. (2011). Statistics alive! (2nd ed.). Thousand Oaks, CA: Sage.

· Assessment Instructions

Answer the questions below, following the Submission Requirements as specified at the end of the assessment.

Assessment Concepts
Question	Topic
Question 1	Ballpark and Exact Median
Question 2	Mode, Median, Mean, and Skew
Question 3	Range, Variance, and Standard Deviation
Question 4	SPSS: Range, Variance, and Standard Deviation
Question 5	Percent Area and the Normal Curve
Question 6	z Scores
Question 7	SPSS: Central Tendency and Z Scores
Question 8	Mutually Exclusive Outcomes
Question 9	Addition and Multiplication Theorems
Question 10	Probabilities: Dichotomous Events
Question 11	Probabilities: Using the Binomial Table

Question 1

Fifty employees were surveyed on their overall job satisfaction on a scale of 1 (not at all satisfied) to 10 (extremely satisfied). Using the below data, calculate the following:

· Start at the bottom of the table to determine the approximate median.

· Use the median formula to determine the exact median.

Job Satisfaction
Job Satisfaction Score	Frequency
10	2
9	8
8	13
7	10
6	7
5	4
4	2
3	2
2	1
1	1

Question 2

Given the following data set:

4, 2, 2, 2, 1, 1, 4, 5, 1, 3, 3, 3, 1, 2, 2, 2, 1, 4, 4, 3, 3, 2, 1, 2, 1.

Find the:

· Mode.

· Median (ballpark).

· Mean.

Are these scores normally distributed, positively skewed, or negatively skewed? Do you expect the mean to be higher or lower than the median?

Question 3

Consider the following set of scores taken from a sample of students:

3, 45, 4, 41, 14, 75, 40, 11, 9, 5, 21, 61, 48, 61, 29, 51, 44, 67, 39, 23, 45, 57, 60, 63, 62.

Find the following:

· Range.

· Variance.

· Standard deviation.

Be sure to show your work.

Question 4

Complete the following steps:

· Open the SPSS file assessment2a.sav linked in the Resources under the Required Resources heading.

· At the top of the screen, click on Analyze, select Descriptive Statistics, then select Descriptives.

· Click on Score, then click on the arrow to send it over to the right side of the table. Select Options, check the boxes next to Variance and Range, and click Continue.

· Click OK and copy and paste the descriptive statistics table to your Word document.

Question 5

Consider the mean combined SAT score for high school seniors is 1500, and the standard deviation is 250. Calculate the percentage of students who scored at the following levels:

· Below 1000.

· Above 1750.

Question 6

For homes sold in the past year, the average number of days on the market (DOM) was 266 days. During this time, DOM was normally distributed, with a standard deviation of 12 days. The Carmichaels sold their house in 245 days. Using the Area Under Normal Curve Table document linked in the Resources under the Required Resources heading, what percentage of homeowners:

· Sold their home at the same point or earlier than the Carmichaels?

· Sold their home at a later point than the Carmichaels?

· Sold their home between 245 days and the average DOM?

Question 7

Complete the following steps:

· Open the SPSS file assessment2b.sav linked in the Resources under the Required Resources heading.

· At the top of the screen, click on Analyze, select Descriptive Statistics, then select Descriptives.

· Click on each variable (q1, q2, q3, q4), then click on the arrow to send each over to the right side of the table. Check the box next to save standardized values as variables.

· Select Options, check the boxes next to Mean and Standard Deviation, and deselect all other boxes. Click on Continue.

· Click OK and copy and paste the descriptive statistics table to your Word document.

· Go back to the Variable View in SPSS, and you will see that the z scores have been added to the file. Paste a screenshot of the Variable View, showing the z scores, into your Word document.

Question 8

Consider the following events. If the outcomes are mutually exclusive, type "yes." If the outcomes are not mutually exclusive, type "no."

· Turning right or turning left.

· Studying Spanish and studying Italian.

· Flipping heads on a coin or flipping tails on a coin.

· Drawing an eight from a deck of cards or drawing a king from a deck of cards.

· Riding a bike or wearing a hat.

Question 9

Consider the following events. If the addition theorem applies, type "AT." If the multiplication theorem applies, type "MT":

· Drawing either a heart or a diamond from a deck of cards

· Either winning or losing a bet.

· Drawing (with replacement) a heart on three successive draws from a deck of cards.

· Rolling a six on three successive rolls of a die.

Question 10

Jane flips a coin 10 times, and each time it lands on heads. What is the probability that the 11th flip will land on heads as well?

Question 11

You have drawn nine cards. Using the Probability Binomial Table linked in the Resources under the Required Resources heading, calculate the following probabilities:

· Four or more cards will be black.

· Two or three cards will be black.

· Zero, one, or two cards will be black.

· Five cards will be black.

Submission Requirements

· Submit all answers in one Word document (do not submit multiple files).

· Show your work for questions that require calculations.

· Ensure your answer to each problem is clearly visible (you may want to highlight your answer or use a different font color to set it apart).