PSYC FPX 4700 Assessment 2 Central Tendency and Probability
PSYC FPX 4700 Assessment 2 Central Tendency and Probability
Name
Capella University
PSYC FPX 4700 Statistics for the Behavioral Sciences
Prof. Name
Date
PSYC FPX 4700 Assessment 2: Central Tendency and Probability
PSYC FPX 4700 Assessment 2 focuses on the statistical concepts psychologists use to organize, describe, and interpret research data. The assessment covers central tendency, variability, probability, conditional probability, normal distributions, and z scores. You will work with measures such as the mean, median, mode, range, variance, and standard deviation while using Excel and JASP to perform and verify statistical calculations. Understanding these concepts helps researchers summarize datasets, compare groups, evaluate probability, and interpret how individual scores relate to an overall distribution.
What Is Covered in PSYC FPX 4700 Assessment 2?
This assessment requires you to apply statistical concepts to several research-based scenarios. You will calculate descriptive statistics, interpret tables, determine probabilities, work with normally distributed data, and calculate standardized scores.
The major areas covered include:
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Mean, median, and mode
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Distribution shape and skewness
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Range, variance, and standard deviation
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Descriptive statistics in Microsoft Excel
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Descriptive statistics in JASP
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Simple and conditional probability
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Independent probability events
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Normal distributions
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Z scores
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Interpretation of statistical results
Complete the problems in the provided Word document and clearly identify your final answers. For calculation-based questions, show the steps used to reach each answer so that the statistical reasoning is easy to follow.
Problem Set 2.1: Characteristics of the Mean
This section focuses on describing a distribution using measures of central tendency. The mean, median, and mode help identify the center or most representative values within a dataset.
A researcher is examining how accurately people can perceive differences in the weight of objects. Twelve participants hold pairs of same-sized objects with different weights and report when they first notice that one object is heavier.
The recorded differences in weight, measured in pounds, are:
4, 8, 9, 5, 12, 7, 6, 15, 10, 4, 8, 8
Calculate the following:
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Mean
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Median
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Mode or modes
After calculating these measures, interpret the relationship between them. The relative positions of the mean, median, and mode can provide useful information about whether a distribution appears approximately symmetrical or shows positive or negative skewness.
When the measures are relatively close together, the distribution may be approximately symmetrical. When the mean is pulled noticeably higher or lower than the median, the difference may indicate skewness.
Problem Set 2.2a: Interpreting Means in a Chart
This section evaluates your ability to compare mean scores across different groups.
Gilman et al. (2008) examined general life satisfaction among 1,338 adolescents from Ireland, the United States, China, and South Korea. The researchers used the Multidimensional Students’ Life Satisfaction Scale (MSLSS). Higher scores indicate greater reported life satisfaction.
| 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 |
Compare the means to determine which group reported the highest and lowest average life satisfaction.
The lowest mean represents the group with the lowest average life satisfaction, whereas the highest mean represents the group with the highest average life satisfaction. Rather than focusing on the number of participants in each group, compare the numerical mean scores shown in the table.
Problem Set 2.2b: Understanding Standard Deviations in a Chart
Standard deviation describes the amount of variation within a set of scores. A small standard deviation indicates that scores are relatively close to the mean, while a larger standard deviation indicates greater spread.
Salska et al. (2008) investigated height preferences among heterosexual individuals using dating profiles from Yahoo! Personals. Their research examined acceptable height ranges for potential dating partners.
| 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 |
To determine which group demonstrated greater variability overall, compare the standard deviations rather than the means.
Because a higher standard deviation represents greater variability, the group with the consistently larger SD values demonstrated more variation in reported height preferences.
Problem Set 2.3: Range, Variance, and Standard Deviation in Excel
This section requires you to use Microsoft Excel to calculate descriptive statistics from raw data.
The dataset represents the number of likes received by individual Facebook posts:
45, 789, 16, 5, 486, 1, 87, 18, 48, 1
You will calculate:
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Range
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Mean
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Variance
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Standard deviation
First, make sure the Analysis ToolPak is available in Microsoft Excel. Enter Data in cell A1 and enter the ten scores in cells A2 through A11.
From the Excel Data menu, select Data Analysis, choose Descriptive Statistics, and enter the data range:
$A$2:$A$11
Select Summary statistics and run the analysis. Excel will generate a descriptive statistics table containing the requested measures.
Transfer the appropriate results to the Word document and clearly identify the final range, mean, variance, and standard deviation.
Problem Set 2.4: Range, Variance, and Standard Deviation in JASP
JASP provides another way to calculate descriptive statistics from the same type of dataset. For this activity, use the likes.jasp dataset containing information about Facebook post likes.
Open the dataset in JASP and select Descriptives. Move the Likes variable into the Variables box and select Transpose descriptives table if required by the assessment instructions.
Under Statistics, select:
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Mean
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Standard deviation
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Variance
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Range
Remove statistics that are not required and review the resulting table.
Copy the relevant table into your Word document and clearly identify the requested values.
You should also compare the mean obtained from JASP with the mean calculated in Problem Set 2.3. When the same data are entered correctly and the same type of statistic is requested, Excel and JASP should generally produce the same descriptive statistic.
Problem Set 2.5: Probability and Conditional Probability
Probability describes how likely an event is to occur. In psychological research, probability can be used to estimate the likelihood of selecting participants with particular characteristics.
For this activity, a hypothetical student population consists of new and returning students who live either on campus or off campus. Use the population table provided with the assessment to calculate each probability.
For a simple probability, divide the number of individuals meeting the specified condition by the total population:
P(A) = Number of favorable outcomes ÷ Total number of outcomes
Conditional probability uses a different denominator. The condition following the word “given” determines the relevant subgroup:
P(A | B) = P(A and B) ÷ P(B)
Calculate the following:
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Probability of selecting a new student.
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Probability of selecting a returning student.
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Probability of selecting a student who lives on campus.
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Probability of selecting a student who lives off campus.
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Probability of selecting a new student, given that the student lives off campus.
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Probability of selecting a returning student, given that the student lives on campus.
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Probability of selecting a new student, given that the student lives on campus.
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Probability of selecting a returning student, given that the student lives off campus.
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Probability of selecting a student who lives on campus, given that the student is a new student.
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Probability of selecting a student who lives off campus, given that the student is a new student.
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Probability of selecting a student who lives on campus, given that the student is a returning student.
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Probability of selecting a student who lives off campus, given that the student is a returning student.
The most important step is identifying the condition after “given.” That condition establishes the denominator used in the conditional probability calculation.
Problem Set 2.6: Determining Probability
This section applies probability to marriage outcomes. According to National Center for Health Statistics information cited in the assessment, approximately 6% of women had married for the first time by age 18, 50% by age 25, and 74% by age 30.
For this exercise, assume that the marriage outcomes of two daughters are independent.
When two independent events must both occur, multiply their probabilities:
P(A and B) = P(A) × P(B)
Using the probabilities provided in the assessment, calculate the probability that both daughters had married:
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By age 18
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By age 25
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By age 30
Show each calculation clearly and convert the resulting decimal values into percentages where appropriate.
Problem Set 2.7: Understanding the Normal Distribution
A normal distribution is a symmetrical, bell-shaped distribution in which observations tend to cluster around the mean. The mean identifies the center of the distribution, while the standard deviation describes its spread.
Z scores allow researchers to determine how far a score is from the mean in standard deviation units. Once the appropriate z score is identified, it can be converted into a raw score using:
X = M + z(SD)
In this problem, Stillman et al. examined how undergraduate students rated jokes on a scale from 1 to 21. For a lawyer joke, the reported statistics were:
M = 14.48
SD = 4.38
The sample included 86 undergraduate students, and the ratings are assumed to follow a normal distribution.
Determine the rating that represents the cutoff for the top 10% of scores. Use the appropriate z score for the upper 10% and substitute the mean and standard deviation into the raw-score formula.
The problem also asks you to estimate how many of the 86 students gave the joke a rating of at least 10. Use the normal distribution to determine the relevant proportion and then apply that proportion to the sample size.
Show the z-score and raw-score calculations so that the reasoning behind your answer is clear.
Problem Set 2.8: Calculating Z Scores in JASP
The final problem set focuses on calculating standardized scores using JASP.
The ratings.jasp dataset contains ratings from senior citizens who evaluated how much they trust the Internet on a scale from 1, representing strong distrust, to 10, representing complete trust.
Open the dataset in JASP and locate the Rating variable. Create a new calculated column for standardized scores.
The general workflow is:
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Select the + sign beside the Rating column.
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Name the new column Z scores.
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Select Create Column.
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Locate the zScores(y) function.
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Replace the placeholder variable with Rating.
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Select Compute column.
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Review the resulting z-score column.
A z score shows the location of an observation relative to the sample mean. A score with a z value of 0 is exactly equal to the mean.
For the assessment question asking which rating is closest to a z score of 0, identify the rating value that is closest to the dataset’s mean.
Key Statistical Concepts for PSYC FPX 4700 Assessment 2
Understanding the difference between central tendency and variability is essential for completing this assessment successfully. Central tendency describes the center of a dataset, while variability describes how much the scores differ from one another.
The mean is calculated by adding all observations and dividing by the number of observations. The median is the middle value after the data are placed in numerical order. The mode is the value that occurs most frequently.
Variability is commonly described using the range, variance, and standard deviation. The range measures the difference between the highest and lowest observations. Variance measures squared deviations from the mean, while standard deviation is the square root of variance and is expressed in the same units as the original measurements.
Probability provides a numerical way to describe the likelihood of an event. Conditional probability goes one step further by considering an additional condition. Normal distributions are particularly useful because the mean and standard deviation can be used to estimate the proportion of observations falling above or below particular values.
Using Excel and JASP for Statistical Calculations
Excel and JASP can make statistical analysis more efficient by automatically calculating descriptive statistics and standardized scores. However, software does not replace the need to understand what each statistic means.
Before interpreting a result, verify that:
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The correct dataset is being used.
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The appropriate variable has been selected.
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The full intended data range is included.
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Missing or incorrectly entered values have been checked.
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The requested statistical measure is selected.
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The output is interpreted using the correct formula or statistical concept.
If identical data are entered correctly into Excel and JASP and the same statistical definition is used, the resulting descriptive statistics should generally agree.
Common Mistakes to Avoid
One common mistake is confusing variance with standard deviation. Variance is expressed in squared units, whereas standard deviation is expressed in the original units.
Another frequent error occurs with conditional probability. Students may use the total population as the denominator even when the question includes the phrase “given that.” In conditional probability, the stated condition determines the relevant population.
It is also important not to confuse a z score with a raw score. A z score describes a position in standard deviation units, while a raw score represents the actual observed value.
Frequently Asked Questions About PSYC FPX 4700 Assessment 2
What is PSYC FPX 4700 Assessment 2 about?
PSYC FPX 4700 Assessment 2 focuses on fundamental statistical concepts used in psychological research. The assessment includes central tendency, variability, probability, conditional probability, normal distributions, and z scores.
What are the three measures of central tendency?
The three primary measures of central tendency are the mean, median, and mode. The mean represents the arithmetic average, the median is the middle value in an ordered dataset, and the mode is the most frequently occurring value.
How do mean, median, and mode help identify skewness?
Comparing the mean, median, and mode can provide clues about distribution shape. When the measures are relatively close, the distribution may be approximately symmetrical. When the mean is pulled substantially away from the median, the distribution may be skewed.
What does standard deviation measure?
Standard deviation measures how much individual observations vary around the mean. A larger standard deviation indicates greater dispersion, while a smaller standard deviation indicates that observations tend to cluster more closely around the mean.
What is the difference between variance and standard deviation?
Variance is based on squared deviations from the mean. Standard deviation is the square root of variance. Unlike variance, standard deviation uses the same measurement units as the original data.
What is conditional probability?
Conditional probability measures the likelihood of one event occurring when another event or condition is already known. It is commonly written as P(A | B) and read as “the probability of A given B.”
How do you calculate conditional probability?
The general formula is:
P(A | B) = P(A and B) / P(B)
The condition after “given” determines the denominator.
What is a normal distribution?
A normal distribution is a symmetrical, bell-shaped distribution centered around its mean. In a standard normal distribution, the mean is 0 and the standard deviation is 1.
What does a z score of 0 mean?
A z score of 0 means that the raw score is exactly equal to the dataset’s mean. Scores above the mean have positive z scores, while scores below the mean have negative z scores.
Why are Excel and JASP used in this assessment?
Excel and JASP can automate statistical calculations, organize data, and help researchers verify results. Using statistical software also reduces the likelihood of arithmetic errors when working with larger datasets.
Why might Excel and JASP produce different results?
If the same dataset produces different results, check the selected data range, variable definitions, missing values, and statistical options. Differences can occur when different formulas or versions of statistics are selected. Correctly analyzing identical data with equivalent settings should generally produce matching results.
How should calculations be presented in PSYC FPX 4700 Assessment 2?
Show the relevant formula, substitute the available values, complete the calculation, and clearly identify the final result. This makes it easier for the evaluator to see both the statistical reasoning and the final answer.
References
Centers for Disease Control and Prevention, National Center for Health Statistics. (2009). First marriage patterns in the United States. 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
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/
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
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