PSYC FPX 4700 Assessment 2 Central Tendency and Probability
Student Name
Capella University
PSYC FPX 4700 Statistics for the Behavioral Sciences
Prof. Name
Date
PSYC FPX 4700 Assessment 2: Central Tendency and Probability
Central tendency, variability, probability, conditional probability, and normal distributions are important concepts in psychological research because they help researchers summarize data and understand the likelihood of different outcomes. In this assessment, you will calculate and interpret measures such as the mean, median, mode, range, variance, and standard deviation. You will also apply probability formulas, interpret normally distributed data, and use Excel and JASP to analyze statistical information.
Complete all problems in this Word document. Do not submit additional files unless specifically instructed. For problems that require calculations, show your work clearly. Make sure each final answer is easy to identify. You may highlight your answers or use a different font color to distinguish them from your calculations and explanations.
Problem Set 2.1: Characteristics of the Mean
Criterion: Describe a distribution.
Read the research scenario below and use the data provided to answer the questions.
A researcher is studying how people perceive differences in weight. A sample of 12 participants is asked to hold pairs of objects that differ in weight but are the same size, with one object placed in each hand. Participants report when they first notice that one object is heavier than the other.
The differences in weight, measured in pounds, are:
4, 8, 9, 5, 12, 7, 6, 15, 10, 4, 8, 8
Use these data to calculate and identify the following measures of central tendency:
- Mean: ______
- Median: ______
- Mode(s): ______
Based on the relationship among the mean, median, and mode, describe the shape of the distribution. Explain how these three measures help you determine whether the distribution is approximately symmetrical, positively skewed, or negatively skewed.
Problem Set 2.2a: Interpreting Means in a Chart
Criterion: Interpret means in a chart.
General life satisfaction can vary across cultures and demographic groups. Gilman and colleagues (2008) examined general life satisfaction among 1,338 adolescents from two individualistic nations, Ireland and the United States, and two collectivist nations, China and South Korea.
Participants completed the Multidimensional Students’ Life Satisfaction Scale (MSLSS). Higher mean scores indicate greater reported life satisfaction.
The mean MSLSS scores are presented below:
| Nation | Men | Women |
|---|---|---|
| United States | 4.39 | 4.61 |
| Ireland | 4.37 | 4.64 |
| China | 4.41 | 4.56 |
| South Korea | 3.92 | 3.78 |
Answer the following questions by comparing the mean scores in the table.
Among which group was general life satisfaction lowest on average? ______
Among which group was general life satisfaction highest on average? ______
Briefly explain how you identified the highest and lowest groups using the mean scores.
Problem Set 2.2b: Understanding Standard Deviations in a Chart
Criterion: Interpret standard deviations in a chart.
Standard deviation describes how much individual scores vary around the mean. A larger standard deviation indicates greater variability, while a smaller standard deviation indicates that scores tend to be more closely grouped around the average.
Salska and colleagues (2008) investigated height preferences among dating partners. In their first study, the researchers reviewed Yahoo! Personals profiles from heterosexual individuals living within 250 miles of Los Angeles, California. They recorded participants’ acceptable ranges for the height of potential dating partners.
The results are summarized below:
| Height Preference | Women: M | Women: SD | Men: M | Men: SD |
|---|---|---|---|---|
| Shortest acceptable height, inches | 68.9 | 2.6 | 60.6 | 3.7 |
| Tallest acceptable height, inches | 75.3 | 2.2 | 69.8 | 2.7 |
Question: Overall, did men or women show greater variability in their responses?
Explain your answer by comparing the standard deviations for men and women. Remember that the group with the larger standard deviations demonstrated greater variability in height preferences.
Problem Set 2.3: Range, Variance, and Standard Deviation in Excel
Criterion: Calculate measures of variability in Excel from a group of raw scores.
Use the following sample data representing the number of likes per Facebook post:
45, 789, 16, 5, 486, 1, 87, 18, 48, 1
Use Microsoft Excel to calculate descriptive statistics, including the range, mean, variance, and standard deviation.
First, make sure the Data Analysis ToolPak is installed in Excel. If you need assistance installing the ToolPak, use Microsoft’s instructions for loading the Analysis ToolPak in Excel.
Enter the data into a new Excel worksheet. In cell A1, enter Data. Enter the ten scores in cells A2 through A11.
Next, select Data Analysis from the Data toolbar and choose Descriptive Statistics. Select OK and enter the following input range:
$A$2:$A$11
Make sure Summary statistics is selected before choosing OK. Excel will create a new worksheet containing the descriptive statistics.
Copy the descriptive statistics table into the appropriate section of the Word document.
Clearly identify the following values:
- Range: ______
- Mean: ______
- Variance: ______
- Standard deviation: ______
Highlight the range, mean, and standard deviation so that your final answers are easy to identify.
Problem Set 2.4: Range, Variance, and Standard Deviation in JASP
Criterion: Calculate measures of variability in JASP.
Use the likes.jasp dataset for this activity. The dataset contains sample information about the number of likes per Facebook post.
Download and open the likes.jasp file in JASP. Follow these steps to obtain the required descriptive statistics.
- Select Descriptives from the JASP toolbar.
- Select Likes and use the arrow to move it into the Variables box.
- Select Transpose descriptives table.
- Open the Statistics menu.
- Select Mean, Standard deviation, Variance, and Range.
- Deselect any statistics that are not required.
- Copy and paste the resulting descriptive statistics table into the Word document.
- Clearly highlight the range, mean, and standard deviation.
Question: Does the mean calculated in JASP equal the mean calculated in Problem Set 2.3?
Answer: ______
Briefly explain whether the results agree and why the same dataset should produce the same descriptive statistics when analyzed correctly in different statistical programs.
Problem Set 2.5: Probability and Conditional Probability
Criterion: Compute probability.
Probability allows researchers to estimate how likely a particular event is to occur. In psychological and social science research, probability can be used to examine the likelihood of selecting individuals with particular characteristics from a population.
For this activity, one student will be selected from a hypothetical population consisting of new and returning students who live either on campus or off campus. Use the student-population table provided with the assessment to calculate the requested probabilities.
For simple probability, divide the number of individuals who meet the specified condition by the total number of individuals in the population. For conditional probability, use the relevant subgroup as the denominator.
PSYC FPX 4700 Assessment 2 Central Tendency and Probability
Answer the following questions:
What is the probability of selecting a new student? ______
What is the probability of selecting a returning student? ______
What is the probability of selecting a student who lives on campus? ______
What is the probability of selecting a student who lives off campus? ______
What is the probability of selecting a new student, given that the student lives off campus? ______
What is the probability of selecting a returning student, given that the student lives on campus? ______
What is the probability of selecting a new student, given that the student lives on campus? ______
What is the probability of selecting a returning student, given that the student lives off campus? ______
What is the probability of selecting a student who lives on campus, given that the student is a new student? ______
What is the probability of selecting a student who lives off campus, given that the student is a new student? ______
What is the probability of selecting a student who lives on campus, given that the student is a returning student? ______
What is the probability of selecting a student who lives off campus, given that the student is a returning student? ______
When calculating conditional probability, pay particular attention to the condition stated after the word “given.” That condition determines the appropriate denominator.
Problem Set 2.6: Determining Probability
Criterion: Determine probability.
The likelihood of marriage by a particular age can be expressed as a probability. According to a National Center for Health Statistics (NCHS) report published by the Centers for Disease Control and Prevention (CDC), approximately 6% of women in the United States had married for the first time by age 18, 50% had married by age 25, and 74% had married by age 30.
Assume that the marriage outcomes of two daughters are independent for purposes of this exercise.
To determine the probability that both daughters will have married by a particular age, multiply the probability for one daughter by the probability for the second daughter.
Calculate the probability that both daughters will have married by each of the following ages:
By 18 years of age: ______
By 25 years of age: ______
By 30 years of age: ______
Show your calculations and convert the final probabilities into percentages when appropriate.
Problem Set 2.7: Understanding the Normal Distribution
Criterion: Solve problems involving normal distributions and probabilities.
A normal distribution is a symmetrical, bell-shaped distribution in which scores tend to cluster around the mean. The standard deviation indicates how far individual observations typically fall from the mean. Z scores and standard normal distribution tables can be used to estimate the proportion of observations that fall above or below a particular score.
Judging the Humorousness of “Lawyer” Jokes
Stillman et al. (2007) examined how participants rated different jokes. A group of 86 undergraduate students rated jokes on a scale from 1 (very unfunny) to 21 (very funny).
Participants rated a lawyer joke with a mean score of 14.48 and a standard deviation of 4.38, reported as:
M = 14.48, SD = 4.38
Assume that the ratings are normally distributed.
What rating represents the cutoff for the top 10% of participant ratings for this joke? ______
Use the appropriate z score for the upper 10% of a normal distribution and apply the formula for converting a z score to a raw score:
X = M + z(SD)
How many of the 86 undergraduate students gave the joke a rating of at least 10? ______
Show your calculations and explain how the normal distribution was used to estimate the number of participants.
Problem Set 2.8: Calculating Z Scores in JASP
Criterion: Calculate z scores using JASP.
Use the ratings.jasp dataset for this activity. The dataset contains ratings from a sample of senior citizens who evaluated how much they trust the Internet on a scale from 1 to 10, where 1 represents “really distrust it” and 10 represents “completely trust it.”
Open the ratings.jasp dataset in JASP and calculate standardized z scores for the Rating variable.
Follow these steps:
- Open ratings.jasp in JASP.
- Locate the column labeled Rating.
- Select the + sign next to the Rating column.
- Enter Z scores as the name of the new column.
- Select Create Column.
- Use the scrollbar in the formula box to locate zScores(y).
- Select Rating and drag it into the formula box so that it replaces the placeholder value.
- Select Compute column.
- Review the newly created z-score column.
- Paste a screenshot of the dataset showing the calculated z scores into the Word document.
Question: Which rating value is closest to a z score of 0?
Answer: ______
A z score of 0 represents a score that is exactly equal to the sample mean. Therefore, identify the rating that is closest to the mean of the dataset.
Key Statistical Concepts to Review
Before completing this assessment, review the difference between measures of central tendency and measures of variability. The mean, median, and mode describe the center or most typical characteristics of a dataset, while the range, variance, and standard deviation describe how widely scores are distributed.
Probability measures the likelihood that an event will occur. Conditional probability focuses on the likelihood of an event when additional information about the situation is known. Normal distributions provide another important statistical framework because researchers can use the mean and standard deviation to estimate the proportion of observations that fall within particular ranges.
For calculations involving Excel or JASP, verify that the correct variable and dataset are selected before interpreting the results. When the same raw data are entered correctly, different statistical programs should generally produce equivalent descriptive statistics, allowing researchers to verify their calculations.
Frequently Asked Questions
What is central tendency in statistics?
Central tendency refers to statistical measures used to describe the center or typical value of a dataset. The three commonly used measures are the mean, median, and mode.
What is the difference between mean, median, and mode?
The mean is calculated by adding all scores and dividing the total by the number of scores. The median is the middle value after scores are arranged in order. The mode is the value that occurs most frequently.
How can mean, median, and mode describe the shape of a distribution?
The relative positions of the mean, median, and mode can provide clues about the shape of a distribution. When the three values are relatively close, the distribution may be approximately symmetrical. A mean that is substantially higher or lower than the median can indicate skewness.
What does standard deviation tell you?
Standard deviation measures the amount of variability in a dataset. A larger standard deviation means that scores are more spread out around the mean, while a smaller standard deviation indicates that scores are more closely clustered around the mean.
What is the difference between variance and standard deviation?
Variance represents the average squared deviation from the mean. Standard deviation is the square root of the variance and is expressed in the same measurement units as the original data.
What is conditional probability?
Conditional probability describes the likelihood that an event will occur when another condition is already known. It is commonly written as P(A | B), meaning the probability of event A given event B.
What is a normal distribution?
A normal distribution is a symmetrical, bell-shaped distribution in which observations are concentrated around the mean. In a standard normal distribution, the mean is 0 and the standard deviation is 1.
What is a z score?
A z score indicates how many standard deviations a particular score is above or below the mean. A z score of 0 means that the score is exactly equal to the mean.
Why are Excel and JASP useful for statistical analysis?
Excel and JASP can quickly calculate descriptive statistics and reduce the amount of manual computation required. They also help researchers organize, analyze, and verify quantitative data.
What should I do if my Excel and JASP results are different?
First, verify that the same data were entered into both programs and that the same statistical measures were selected. Check for missing values, data-entry errors, incorrect ranges, or differences in the way variables were defined. Correctly analyzed identical datasets should generally produce matching descriptive statistics.
References
Centers for Disease Control and Prevention. (2009). First marriage patterns in the United States. National Center for Health Statistics. https://www.cdc.gov/nchs/
Gilman, R., Huebner, E. S., & Laughlin, J. E. (2008). A first study of the Multidimensional Students’ Life Satisfaction Scale with adolescents. Social Indicators Research, 86, 229–239. https://doi.org/10.1007/s11205-007-9181-5
Salska, I., Frederick, D. A., Pawlowski, B., Reilly, A., Lomba, A., & Symons, D. (2008). Conditional mate preferences: Factors influencing preferences for height in men and women. Personality and Individual Differences, 45(5), 401–406. https://doi.org/10.1016/j.paid.2008.05.007
PSYC FPX 4700 Assessment 2 Central Tendency and Probability
Stillman, T. F., Baumeister, R. F., Lambert, N. M., Crescioni, A. W., DeWall, C. N., & Fincham, F. D. (2009). Alone and without purpose: Life loses meaning following social exclusion. Journal of Experimental Social Psychology, 45(4), 686–694. https://doi.org/10.1016/j.jesp.2009.03.007
JASP Team. (2026). JASP: A fresh way to do statistics [Computer software]. https://jasp-stats.org/
Microsoft. (2026). Load the Analysis ToolPak in Excel. Microsoft Support. https://support.microsoft.com/