At the top of the third page, you will see the start of a table. Under the heading that begins with X, you will add rows for the student scores, starting with 18 and working down to 6. Calculate the X-M and (X-M)2 values for each score. At the bottom of the table, calculate the values for ∑X, ∑(X-M), and ∑(X-M)2. You will then have the numbers needed to calculate the variance.

For section 4B, you are provided with the headings for a table. Under the headings “Really Worse,” “Worse,” etc. you will add a row. In this row, provide a range of scores for each performance range. Determine the score ranges for each category starting with the Typical range. The scores for the Typical range will range from one standard deviation below the mean to one standard deviation above the mean.  You also will add a row under the heading “Converted to Absolute Value.” Convert the score ranges to ranges of percentile ranks for each category.

When you answer question #2 below this table, look at the percentage of the students who scored in the Typical range, and consider their level of mastery of the content and possible next steps for them.

In section 4C #3, choose from Worse/Below average, Typical/Average, and Better/Above average.





Please answer the questions by typing your responses after each question.  Save the file when you are finished and submit it using the assignment link in Unit 5. You will have only ONE attempt to complete this Application Quiz.


In the presentation and Case Study Exercise for Unit 3, we used a scenario where you were an employee in student affairs at a university.  In those scenarios you examined the role of student activities to enhance freshmen transition and the perceived stress of a group of freshmen.  

It has been shown that social support is a buffer that helps to protect against stress. So, in order to determine how to help your group of freshmen, you asked them to complete another measure called the Social Support Survey.  It is a norm-referenced, standardized measure that was normed on a representative sample of college freshmen.  The Social Support Survey consists of 20 questions that ask students about the supports they use.  Each question is answered either yes, sometimes, or no.  

  1. What type of response format is being used? (2 points)

When the survey is complete, you assign points for each response with 2 = Yes, 1 = sometimes, and 0 = No.  You sum the scores for each item and obtain a total support score for each student.  High scores suggest strong support systems and low scores suggest poor/weak social support systems.  

  • What level of measurement is being used? (1 point)

Forty freshmen complete the Social Support Scale and their scores are as follows:

11       20       12       10           12       17       19           14

22       15       14       15           18       14       11           13

16       25        6       19           37       25       20           16

 9         3       13       20           11       12       11           10      

 7        27       18       31           15       20       18           38

Using these scores, create a grouped and cumulative frequency distribution table that has nine intervals and enter the data below (42 points):

Class Intervalfcf
               N =                                                              i =      

Using the table you’ve created, answer the following questions based on the class intervals:

  1. The university recommends that students receiving scores below 12 be selected to participate in a “Freshman Connection Program” that helps students develop support systems among peers on campus.  Based on your results, how many students would be recommended for the program? (1 point)
  • One student you are concerned about, Sally, scored 11.  
  1. How many freshmen perceived that they had a poorer social support system than Sally? (1 point)
  • How many freshmen perceived that they had a stronger social support system than Sally? (1 point)

3.  What might you conclude about Sally’s perception of her social support system? (2 points)


This is the second set of Case Study Exercises (CSEs). These exercises are provided to assess your skills and to provide an opportunity to ensure mastery of the content. They should not be attempted until you have read the assigned readings and reviewed the course presentations for Unit 4. When you are ready, please submit the CSEs for review. When you receive your feedback, if everything is correct, you are ready for the Application Quiz #2 in Unit 5! If there are errors, you will be provided with feedback and the opportunity to resubmit the CSEs. No partial credit is applied to the CSEs. Provided that the CSEs were submitted by the unit deadline, the 20 points will be awarded once you have successfully completed the entire exercise. You may retry it as often as necessary until you have strengthened your skills. Since there is a developmental sequence to the acquisition of measurement skills, you must be proficient at each level before continuing to the next unit.


Please answer the questions by typing your responses after each question.  Save the file when you are finished and submit it using the assignment link in Unit 4.

#4-A.  Measures of Central Tendency and Dispersion

You are a math teacher in an elementary school.  In preparation for upcoming benchmark assessments, you do a quick probe of your students’ math skills.  You select 20 items from your recent math unit and administer the assessment.  Your students earn the following scores:


You decide to analyze the results so that you have a better picture of the group and individual performance.  (Please remember to round all answers to two decimal places: ie. 0.00)

  1. What should be your first step?  
  • Which score was obtained by the largest number of people?  
  • What is this score called?
  • What is the N for this distribution/data set?
  • Between what two scores do you need to divide the scores to calculate the median?
  • What is the numerical value of the median?
  • What is the ∑ X?
  • What is the Mean?
  • What is the range?

After reviewing the results you decide to further explore the data and determine the variability within the group.

Complete the following table and then answer the questions below.  (Please remember to round all answers to two decimal places: ie. 0.00)  Don’t worry if the alignment of the table or columns get a little altered when you type; as long as the numbers that are in the cells can be determined you are fine.

∑X=∑ (X-M) =∑ (X-M)2=
  1. What is the variance?
  • What is the standard deviation?

#4-B.  Interpreting Your Distribution

  1. Using your answers from Part A, complete the table below by calculating the relative performance ranges and then converting them to absolute performance.  
Relative Performance Ranges
Really WorseWorseTypicalBetterReally Better
Converted to Absolute Performance
  • What is your interpretation of the performance of your class on this assessment?

#4-C.  The Normal Curve and Normal Distributions

Assume that you have just received the results of your trainees’ performance on a national licensure exam.  The exam is a norm-referenced, standardized test with a mean of 200 and a SD of 25

  1. On this exam, 68.26% of the scores would lie between what two scores?
  • On this exam, 95.44% of the scores would lie between what two scores?
  • Define the performance range for each of these trainees:

Barney who earned a score of 233 –

Marshall who earned a score of 158 –

Sheldon who earned a score of 196 –

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