To apply statistical reasoning in psychology, you must be able to understand and utilize central tendency and probability calculations for various circumstances.

Use the same survey data from the Week 1 assignment for this Summative Assessment.

Continuing in your role as an intern with a community clinic, imagine your supervisor has now requested that you prepare a report for the entire staff of the clinic on the results of the customer satisfaction survey.

Your supervisor has asked you to explain the statistical calculations using language that the entire staff of your community clinic (such as office workers or those who have never had a course in statistics) could understand.

Write a 350- to 525-word report that includes:

• Computation of the mean, median, mode, sum of squares (SS), the variance, and the standard deviation for this sample using the definitional and computational formulas
• Data organized in a table with definitional and computational formulas for each
• A review of your histogram from Week 1, in which you determine whether the mean is greater than, less than, or approximately equal to the median. Justify your answer.
• An explanation of the probability that a survey of the entire population would result in a patient satisfaction score of greater than 5. Justify your answer.

Struggling with where to start this assignment? Follow this guide to tackle your assignment easily!

Step 1: Gather Your Week 1 Data

Use the same customer satisfaction survey data you analyzed in Week 1. This ensures consistency and continuity in your analysis. If you need to revisit your Week 1 submission, refer to your saved document or course portal.

Step 2: Calculate the Descriptive Statistics

You’ll need to compute the following using both definitional and computational formulas:

• Mean (Average)
  Add all scores and divide by the number of responses.
  How to calculate the mean

• Median
  Order the scores and find the middle value. If even number, average the two middle values.
  Median calculator & explanation

• Mode
  Identify the most frequent response.
  How to find the mode

• Sum of Squares (SS)
  SS=Σ(X−M)2SS = Σ(X – M)²SS=Σ(X−M)2 where X is each score and M is the mean.
  Sum of squares explained

• Variance
  Divide the SS by the number of responses (for population) or n-1 (for sample).
  Understanding variance

• Standard Deviation
  Take the square root of the variance.
  Standard deviation breakdown

Step 3: Present Your Work in a Table

Create a clear table showing:

• Each statistic (Mean, Median, etc.)

• The formula used (definitional and computational)

• The actual value from your data

This makes it easy for your supervisor and staff to follow.

Step 4: Analyze Your Histogram from Week 1

• Revisit the histogram you created.

• Compare the mean and median values:

  • If the data is skewed right, the mean > median

  • If skewed left, the mean < median

  • If symmetric, the mean ≈ median

• Justify your analysis based on the shape of the graph.

Skewness and central tendency visual guide

Step 5: Explain the Probability

• State how likely it is (in your opinion) that a full population survey would show satisfaction > 5.

• Use your mean and standard deviation to explain whether scores above 5 are common or rare.

• Consider using normal distribution logic:

  • If your mean is < 5, such scores may be less likely.

  • Support your answer with reasoning, not just numbers.

Intro to probability in stats

Step 6: Write the Report

Keep it between 350–525 words. Use clear, non-technical language so all staff can understand.

Structure:

1. Intro – What’s the purpose of the report?

2. Data Summary – Present your findings (table + description)

3. Histogram Review – Discuss the distribution

4. Probability Interpretation – Explain your reasoning

5. Conclusion – Summarize insights for the staff

Tips for writing statistical reports clearly

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