Lab 1: Central Tendency and Variability

Analyzing Sprint Performance in Elite Athletes

TipHow to Use This Lab Document

For Students:

  1. 📥 Download Lab 1 (Word Format) - Click to download the editable version
  2. Add your name and date in the document header
  3. Complete all questions in Part 2: Your Answers
  4. Include SPSS output where requested
  5. DELETE Part 1 (Instructions) before submitting
  6. Submit only Part 2 (Your Answers) via Canvas

File Naming: Save as LastName_FirstName_Lab01.pdf

PART 1: INSTRUCTIONS

WarningImportant: Delete This Section Before Submission

Part 1 contains the lab instructions and background information. After reading the instructions and completing your work in Part 2, DELETE this entire Part 1 section before submitting your lab.

Due Date & Submission Requirements

Due: One week from assignment date (see Course Schedule for specific deadline)

Submission: Submit your completed lab via Canvas as a single Word document containing only Part 2 (Your Answers)

Deliverables

Your lab submission must include:

  1. Cover Page with:
    • Your name
    • Course number and section
    • Lab title: “Lab 1: Central Tendency and Variability”
    • Date of submission
  2. Responses to All Questions (Parts 1-5):
    • Part 1: Questions 1.1, 1.2, 1.3
    • Part 2: Questions 2.1, 2.2, 2.3
    • Part 3: Questions 3.1, 3.2, 3.3
    • Part 4: Questions 4.1, 4.2
    • Part 5: Question 5.1 (results paragraph)
  3. SPSS Output Tables - Include all relevant output:
    • Frequencies table with descriptive statistics
    • Histogram of sprint times
    • Group comparison table (Means procedure)
    • Any additional tables you created
  4. Written Interpretations in complete sentences for all questions
  • File Type: PDF only (.pdf) - Word documents will not be accepted
  • Font: 12-point, readable font (Times New Roman, Arial, Calibri)
  • SPSS Output: Can be pasted as images or tables (ensure readability)

Before submitting, verify you have:

WarningIncomplete Submissions

Labs missing required components (SPSS output, unanswered questions, or missing interpretations) will receive deductions as specified in the evaluation rubric. Ensure your submission is complete before uploading.

Lab Overview

Learning Objectives

By the end of this lab, you will be able to:

  1. Calculate and interpret the mode, median, and mean for movement science data
  2. Calculate and interpret measures of variability (range, variance, standard deviation)
  3. Identify the most appropriate measures based on data characteristics
  4. Understand how outliers and distribution shape affect descriptive statistics
  5. Use SPSS to compute descriptive statistics
  6. Present and interpret statistical results in a professional format

Scenario

You are a sport scientist working with a national track and field federation. The head coach wants to understand the typical 100-meter sprint performance of their elite athletes to inform training program decisions and identify athletes who may need specialized attention.

The federation has collected sprint times (in seconds) from their training camp assessment. Your task is to analyze these data using measures of central tendency and variability to provide the coach with actionable insights about both the team’s typical performance and the consistency (or variability) of that performance.

Dataset

You will use the Core Dataset for this lab — specifically, the sprint_20m_s variable (20-meter sprint time in seconds) from the session data.

Accessing the Dataset

TipDataset File

For this lab, you will only need the core_session.csv file from the Core Dataset.

Download: Get the file from the SMS book repository at https://github.com/drfurtado/sms/tree/main/data

Dataset Information: For details about the Core Dataset structure, variables, and study background, see the Core Dataset Overview and Core Dataset Codebook in the SMS textbook.

Download the file and save it to your computer, then import it into SPSS from your local folder.

SPSS Access

On Campus: Use SPSS installed in the computer labs
Remote Access: Use Virtual SPSS via Apporto (link available in Canvas)

Section 1: Data Preparation (8 points)

Task 1.1: Import the Data into SPSS

  1. Open SPSS (either on campus or via Apporto)
  2. Import the core_session.csv file into SPSS
NoteNeed Help?

If you’re not sure how to import CSV files into SPSS, refer to the SPSS tutorials on Canvas or ask your instructor for guidance.

Question 1.1 (2 points): How many total observations (rows) are in the session dataset? Report this number.

Task 1.2: Examine the Sprint Time Variable

Before calculating any statistics, you should examine your variable of interest.

  1. In SPSS, go to Analyze → Descriptive Statistics → Frequencies
  2. Select the sprint_20m_s variable
  3. Click Statistics and check: Mean, Median, Mode, Std. deviation, Variance, Minimum, Maximum, Range
  4. Click Continue, then OK

Question 1.2 (3 points): Based on the output, answer:

  1. What is the minimum sprint time recorded?
  2. What is the maximum sprint time recorded?
  3. Do you notice anything unusual about the range of values?

Task 1.3: Visualize the Distribution

Create a histogram to visualize the distribution of sprint times.

  1. Go to Graphs → Legacy Dialogs → Histogram
  2. Select sprint_20m_s as the variable
  3. Check “Display normal curve”
  4. Click OK
NoteNeed Help?

For detailed instructions on creating histograms, refer to the SPSS tutorials on Canvas.

Question 1.3 (5 points):

  1. Include the histogram in your report
  2. Describe the shape of the distribution (symmetric, positively skewed, negatively skewed)
  3. Are there any outliers visible in the histogram? Explain your reasoning.

Section 2: Calculating Descriptive Statistics (44 points)

Task 2.1: Compute Descriptive Statistics

Using SPSS, calculate measures of central tendency and variability for sprint times.

  1. Go to Analyze → Descriptive Statistics → Frequencies
  2. Select sprint_20m_s
  3. Click Statistics and ensure the following are selected:
    • Central Tendency: Mode, Median, Mean
    • Variability: Range, Std. deviation, Variance
  4. Click Continue, then OK
NoteNeed Help?

For step-by-step instructions, see:

Question 2.1 (12 points): Create a table in your report with the following format:

Measure Value (seconds)
Mode
Median
Mean
Range
Variance
Standard Deviation

Include the SPSS output table in your report.

Task 2.2: Interpret the Measures

Question 2.2 (12 points): Answer the following questions in complete sentences:

Central Tendency:

  1. What is the most frequently occurring sprint time (mode)?
  2. What is the middle sprint time value (median)?
  3. What is the average sprint time (mean)?
  4. Are the three measures similar or different? What might this tell you about the distribution shape?

Variability:

  1. What is the range of sprint times? What does this tell you about the spread of performance?
  2. What is the standard deviation? Interpret this value in the context of sprint performance consistency.

Task 2.3: Relationship Between Measures and Distribution

Question 2.3 (11 points): Based on your understanding of descriptive statistics:

  1. In a normal (symmetric) distribution, what is the relationship between mean, median, and mode?
  2. In a positively skewed distribution, how are mean, median, and mode ordered?
  3. Based on your results, does the sprint time distribution appear to be symmetric or skewed? Explain your reasoning using the values you calculated. Note: In Section 2.4 below, you will use formal and visual assessment methods from Chapter 7 to further examine the distribution.
  4. If two athletes both have a mean sprint time of 3.8 seconds, but Athlete A has SD = 0.05s and Athlete B has SD = 0.25s, what does this tell you about the consistency of their performances?

Task 2.4: Formal Assessment of Distribution Shape

In Chapter 7 (The Normal Distribution), you learned about formal statistical procedures and visual methods for assessing whether data follow a normal distribution. Now apply those techniques to the sprint time data.

Step 1: Calculate Skewness and Kurtosis

  1. Go to Analyze → Descriptive Statistics → Descriptives
  2. Select sprint_20m_s
  3. Click Options
  4. Check: Kurtosis and Skewness (SPSS will automatically provide both the values and their standard errors)
  5. Click Continue, then OK
  6. From the SPSS output, record:
    • Skewness value and its Std. Error
    • Kurtosis value and its Std. Error
  7. Calculate z-scores using the formulas from Chapter 7:
    • \(z_{\text{skew}} = \frac{\text{Skewness}}{SE_{\text{skew}}}\)
    • \(z_{\text{kurt}} = \frac{\text{Kurtosis}}{SE_{\text{kurt}}}\)
NoteNeed Help with Interpretation?

Review these Chapter 7 sections: - Testing significance of skewness: z-skew - Testing significance of kurtosis: z-kurtosis - Interpreting z-skew and z-kurtosis together

Step 2: Create a Q-Q Plot

  1. Go to Analyze → Descriptive Statistics → Q-Q Plots
  2. Select sprint_20m_s as the variable
  3. Test Distribution: Select Normal
  4. Click OK
NoteNeed Help?

For detailed Q-Q plot instructions, see: - SPSS Tutorial: Normality Assessment - Chapter 7: Q-Q Plots

Question 2.4 (15 points):

  1. Report the following values from SPSS output and your calculations:
    • Skewness, Standard Error of Skewness, and z-skew
    • Kurtosis, Standard Error of Kurtosis, and z-kurtosis
  2. Based on the z-scores and interpretation guidelines from Chapter 7:
    • Is z-skew significant (|z-skew| ≥ 1.96 at α = .05)? What does this tell you about asymmetry?
    • Is z-kurtosis significant (|z-kurtosis| ≥ 1.96 at α = .05)? What does this tell you about tail behavior?
    • Using the interpretation table in Chapter 7, what is the overall assessment of distribution shape?
  3. Include your Q-Q plot in your report. Based on the Q-Q plot pattern:
    • Do the points fall close to the diagonal reference line (suggesting normality)?
    • Or do you see systematic patterns (e.g., upward curve at right, S-shape) suggesting departure from normality?
  4. Combining your visual assessment (histogram from Section 1.3, Q-Q plot) with formal measures (skewness, kurtosis), would you conclude that the sprint time distribution is approximately normal or shows meaningful departure from normality? Justify your answer referencing both the visual and formal evidence.
TipIntegration Tip

As discussed in Chapter 7, visual assessment (histograms and Q-Q plots) should be your primary tool, with formal statistics (skewness, kurtosis) providing supplementary evidence. Consider both together when making your conclusion.

Section 3: Effect of Outliers (18 points)

Background

You discover that three sprint times in the dataset appear to be recording errors—the timing equipment malfunctioned for these trials. The coach wants to know how these outliers affect the team’s “typical” performance.

Task 3.1: Identify Potential Outliers

Examine your histogram and frequency table to identify sprint times that seem unusually high compared to the rest of the data.

Question 3.1 (5 points):

  1. What sprint time value(s) appear to be potential outliers?
  2. How many cases have these extreme values?

Task 3.2: Compare Measures with and without Outliers

For this task, you’ll need to:

  1. Select only the valid sprint times (excluding the outliers you identified)
  2. Recalculate the mean, median, and mode
TipSPSS Tip: Selecting Cases

To exclude outliers temporarily: 1. Go to Data → Select Cases 2. Choose “If condition is satisfied” 3. Click If and enter: sprint_20m_s < [your cutoff value] 4. Click Continue, then OK 5. Recalculate your statistics

Don’t forget to turn selection off when done: Data → Select Cases → All cases

Question 3.2 (12 points): Create a comparison table:

Measure All Data Outliers Removed
Mean
Median
Standard Deviation

Then answer:

  1. Which measure of central tendency (mean or median) changed the most when outliers were removed?
  2. Did the standard deviation increase or decrease when outliers were removed? Why does this make sense?
  3. Which measure was most resistant (least affected) by outliers?

Task 3.3: Recommendation

Question 3.3 (5 points): As the sport scientist, which measure of central tendency would you report to the coach to represent “typical” sprint performance, and should you report the standard deviation calculated with or without outliers? Justify your choices considering:

  • The presence of outliers
  • What the coach needs to know about typical performance AND consistency
  • Which measures best represent the team’s actual performance

Section 4: Applied Analysis (18 points)

Task 4.1: Group Comparison

The Core Dataset includes athletes in a training group and a control group. Compare sprint times between these groups.

  1. Go to Analyze → Compare Means → Means
  2. Put sprint_20m_s in the Dependent List
  3. Put group in the Independent List
  4. Click Options and select: Mean, Median, Std. Deviation
  5. Click Continue, then OK

Question 4.1 (10 points):

  1. Create a table showing the mean and standard deviation for each group
  2. Which group has faster sprint times (lower mean values)?
  3. Which group shows more consistent performance (lower variability)?
  4. Based on both the means and standard deviations, what might this suggest about the effect of the training program?

Task 4.2: Appropriate Measure Selection

Question 4.2 (10 points): For each scenario below, indicate which measure of central tendency (mode, median, or mean) would be most appropriate and explain why:

  1. Scenario A: You’re analyzing shoe sizes worn by basketball players in the NBA to help equipment managers stock the most common sizes.

  2. Scenario B: You’re reporting typical recovery time (in days) after ACL reconstruction surgery, and a few patients had complications that dramatically extended their recovery.

  3. Scenario C: You’re calculating average heart rate during steady-state running for a research study, and the data are normally distributed with no outliers.

  4. Scenario D: You’re analyzing race finishing positions (1st, 2nd, 3rd, etc.) for marathon runners.

Section 5: Communication of Results (12 points)

Task 5.1: Write a Results Paragraph

Question 5.1 (15 points): Write a brief results paragraph (175-225 words) summarizing your findings for the track and field coach. Your paragraph should:

  1. State the measure(s) of central tendency you chose and why
  2. Report the typical sprint time for the team
  3. Report the variability (standard deviation) and what it means for performance consistency
  4. Mention the outlier issue and how you addressed it
  5. Compare the training and control groups (both means and variability)
  6. Provide a clear, practical interpretation the coach can understand
TipExample Format (DO NOT COPY)

“The analysis of 20-meter sprint times revealed that the typical performance was [value] seconds (measure chosen), with a standard deviation of [value] seconds, indicating [interpretation of consistency]. This conclusion is based on [justification]. After identifying and excluding [number] outlier values due to equipment malfunction, [describe finding]. Comparison between groups showed that the training group performed [faster/slower] with [more/less] consistency…”

Evaluation Rubric

Your lab will be graded using the following rubric:

Component Points Criteria
Part 1: Data Preparation 8 Correctly imports data, examines variables, creates appropriate visualizations
Part 2: Descriptive Statistics 44 Accurate calculation of central tendency and variability measures; correct interpretation; understanding of relationships; formal and visual assessment of distribution shape using Chapter 7 methods
Part 3: Outlier Effects 18 Identifies outliers; correctly compares measures with/without outliers; provides justified recommendation
Part 4: Applied Analysis 18 Accurate group comparison of means and variability; appropriate measure selection with clear reasoning
Part 5: Communication 12 Clear, professional writing; accurate reporting of both central tendency and variability; practical interpretation
TOTAL 100

Additional Grading Considerations

  • SPSS Output: All required SPSS output tables must be included (-5 points for each missing table)
  • Formatting: Report should be well-organized with clear section headers (-5 points if poorly formatted)
  • Completeness: All questions must be answered (-5 points per unanswered question)
  • Professional Presentation: Use complete sentences, proper grammar, and appropriate statistical terminology

Resources

SPSS Tutorials (from your textbook)

Textbook Chapters

Canvas Resources

  • SPSS via Apporto (Virtual Lab) - link in Canvas
  • Lab submission portal - Canvas Assignments
NoteAnswer Key Availability

The answer key for this lab will be made available on Canvas after the lab has been graded and returned to all students.

WarningAcademic Integrity

This lab is an individual assignment. While you may discuss general concepts with classmates, all written work and analysis must be your own. Copying from others or sharing your work constitutes academic dishonesty. Do not use AI tools to generate answers. If you have questions, ask your instructor or attend office hours.

Questions?

If you have questions while completing this lab: 1. Review the relevant textbook chapters and SPSS tutorials 2. Attend office hours 3. Post questions in the Canvas discussion forum (do not share answers)

END OF PART 1: INSTRUCTIONS
(Remember to delete Part 1 before submitting!)

PART 2: YOUR ANSWERS

ImportantSubmission Instructions

Complete all questions below and submit ONLY this Part 2 section (delete Part 1 before submitting).

  • Include your SPSS output (paste as images or tables)
  • Write all interpretations in complete sentences
  • Show your work where calculations are required
  • Name your file: LastName_FirstName_Lab01.pdf

Student Information

Name: __________________________________________________

Course & Section: ____________________________________

Date: ___________________________________________

Section 1: Data Preparation (8 points)

Question 1.1 (2 points)

How many total observations (rows) are in the session dataset?

Answer:

 

 

Question 1.2 (3 points)

Based on the SPSS Frequencies output, answer:

  1. What is the minimum sprint time recorded?

Answer:

 

  1. What is the maximum sprint time recorded?

Answer:

 

  1. Do you notice anything unusual about the range of values?

Answer:

 

 

 

Question 1.3 (5 points)

  1. Include your histogram here (paste SPSS output):

 

 

 

 

 

  1. Describe the shape of the distribution (symmetric, positively skewed, negatively skewed):

Answer:

 

 

 

  1. Are there any outliers visible in the histogram?

Answer:

 

 

 

Section 2: Calculating Descriptive Statistics (44 points)

Question 2.1 (12 points)

Create a table with your calculated measures:

Measure Value (seconds)
Mode
Median
Mean
Range
Variance
Standard Deviation

Paste your SPSS output here:

 

 

 

Question 2.2 (12 points)

Central Tendency:

  1. What is the most frequently occurring sprint time (mode)?

Answer:

 

 

  1. What is the middle sprint time value (median)?

Answer:

 

 

  1. What is the average sprint time (mean)?

Answer:

 

 

  1. Are the three measures similar or different? What might this tell you about the distribution shape?

Answer:

 

 

 

 

Variability:

  1. What is the range of sprint times? What does this tell you about the spread of performance?

Answer:

 

 

 

  1. What is the standard deviation? Interpret this value in the context of sprint performance consistency.

Answer:

 

 

 

Question 2.3 (11 points)

  1. In a normal (symmetric) distribution, what is the relationship between mean, median, and mode?

Answer:

 

 

 

  1. In a positively skewed distribution, how are mean, median, and mode ordered?

Answer:

 

 

 

  1. Based on your results, does the sprint time distribution appear to be symmetric or skewed? Explain your reasoning using the values you calculated.

Answer:

 

 

 

 

  1. If two athletes both have a mean sprint time of 3.8 seconds, but Athlete A has SD = 0.05s and Athlete B has SD = 0.25s, what does this tell you about the consistency of their performances?

Answer:

 

 

 

 

Question 2.4 (15 points)

  1. Report the following values from SPSS output and your calculations:

Answer:

Measure Value Std. Error z-score
Skewness ______ ______ ______
Kurtosis ______ ______ ______

Show your z-score calculations:

\(z_{\text{skew}} = \frac{\text{Skewness}}{SE_{\text{skew}}} =\) _____________

\(z_{\text{kurt}} = \frac{\text{Kurtosis}}{SE_{\text{kurt}}} =\) _____________

 

  1. Based on the z-scores and interpretation guidelines from Chapter 7:
    • Is z-skew significant? What does this tell you about asymmetry?
    • Is z-kurtosis significant? What does this tell you about tail behavior?
    • Using the interpretation table in Chapter 7, what is the overall assessment?

Answer:

z-skew interpretation:

 

 

z-kurtosis interpretation:

 

 

Overall assessment:

 

 

  1. Include your Q-Q plot in your report. Based on the Q-Q plot pattern, do the points fall close to the diagonal reference line (suggesting normality) or do you see systematic patterns suggesting departure from normality?

Answer:

(Insert Q-Q plot here)

 

 

 

  1. Combining your visual assessment (histogram from Section 1.3, Q-Q plot) with formal measures (skewness, kurtosis), would you conclude that the sprint time distribution is approximately normal or shows meaningful departure from normality? Justify your answer referencing both the visual and formal evidence.

Answer:

 

 

 

 

 

Section 3: Effect of Outliers (18 points)

Question 3.1 (5 points)

  1. What sprint time value(s) appear to be potential outliers?

Answer:

 

 

  1. How many cases have these extreme values?

Answer:

 

 

Show your calculations for Q1, Q3, IQR, and fences:

 

 

 

Question 3.2 (12 points)

Create a comparison table:

Measure All Data Outliers Removed
Mean
Median
Standard Deviation

Paste your SPSS output here:

 

 

 

Then answer:

  1. Which measure of central tendency (mean or median) changed the most when outliers were removed?

Answer:

 

 

 

  1. Did the standard deviation increase or decrease when outliers were removed? Why does this make sense?

Answer:

 

 

 

  1. Which measure was most resistant (least affected) by outliers?

Answer:

 

 

 

Question 3.3 (5 points)

As the sport scientist, which measure of central tendency would you report to the coach, and should you report the standard deviation calculated with or without outliers? Justify your choices.

Answer:

 

 

 

 

 

Part 4: Applied Analysis (18 points)

Question 4.1 (10 points)

  1. Create a table showing the mean and standard deviation for each group:
Group Mean Sprint Time (seconds) Standard Deviation
Control
Training

Paste your SPSS output here:

 

 

 

  1. Which group has faster sprint times (lower mean values)?

Answer:

 

 

  1. Which group shows more consistent performance (lower variability)?

Answer:

 

 

  1. Based on both the means and standard deviations, what might this suggest about the effect of the training program?

Answer:

 

 

 

 

Question 4.2 (10 points)

For each scenario below, identify which measure of central tendency would be most appropriate and explain why.

a. An NBA equipment manager needs to determine which shoe sizes to stock in the team locker room.

Measure: __________

Justification:

 

 

 

b. A physical therapist is analyzing ACL surgery recovery times, but a few patients had complications that dramatically extended their recovery.

Measure: __________

Justification:

 

 

 

c. A researcher is analyzing heart rate data from steady-state running in a normally distributed sample with no outliers.

Measure: __________

Justification:

 

 

 

d. A race director wants to report the “typical” finishing position for participants in a marathon.

Measure: __________

Justification:

 

 

 

Section 5: Communication of Results (12 points)

Write a brief results paragraph (175-225 words) summarizing your findings for the track and field coach. Your paragraph should:

  1. State the measure(s) of central tendency you chose and why
  2. Report the typical sprint time for the team
  3. Report the variability (standard deviation) and what it means for performance consistency
  4. Mention the outlier issue and how you addressed it
  5. Compare the training and control groups (both means and variability)
  6. Provide a clear, practical interpretation the coach can understand

Your Results Paragraph:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Word Count: __________ (aim for 175-225 words)

Checklist Before Submission

Good luck! 🏃‍♂️📊