SPSS Descriptive Statistics Worked Example

The Question

A tutor wants to summarize the age, weekly study time, and practice-quiz scores of 20 fictional students. Use SPSS to describe the center, spread, and shape of each variable. Then explain what the numbers mean without treating descriptive results as proof of cause and effect.

Copy the Example Data

The first row contains short variable names. Copy the tab-separated block below and paste it into SPSS Data View, beginning in the first cell.

id	age	study_hours	quiz_score
1	18	6	52
2	19	7	55
3	20	7	58
4	20	8	61
5	21	8	60
6	22	8	63
7	19	9	65
8	20	9	67
9	23	10	69
10	24	10	70
11	20	10	72
12	21	11	73
13	22	11	74
14	23	12	76
15	24	12	78
16	25	12	77
17	26	13	81
18	27	14	84
19	28	15	86
20	30	16	89

Set Up the Variables in SPSS

In Variable View, use names without spaces, such as study_hours. Add readable labels such as “Study hours per week.” Set missing-value rules only when the dataset actually uses special codes such as 999; do not invent a missing code after seeing the data.

Run Frequencies from the menus

1. Choose Analyze → Descriptive Statistics → Frequencies.
2. Move age, study_hours, and quiz_score into the Variables box. Leave id out.
3. Select Statistics, then choose Mean, Median, Mode, Std. deviation, Variance, Range, Minimum, Maximum, and Skewness.
4. For variables with many distinct values, clear Display frequency tables so the output stays readable. Keep it selected when individual counts are useful.
5. Select Continue, then OK.

Equivalent SPSS syntax

FREQUENCIES VARIABLES=age study_hours quiz_score
  /STATISTICS=MEAN MEDIAN MODE STDDEV VARIANCE
              SKEWNESS RANGE MINIMUM MAXIMUM
  /ORDER=ANALYSIS.

Saving syntax makes the analysis easier to check and reproduce. SPSS may display slightly different decimal places depending on the variable format.

Which SPSS Descriptive Statistics Procedure Should You Use?

SPSS offers several procedures for descriptive statistics. The best choice depends on the variable type and the output your assignment requires. This worked example uses Frequencies because it can return the mean, median, mode, range, variance, standard deviation, and skewness together.

These procedures may arrange the output differently. When they analyze the same valid cases with the same missing-value rules, matching statistics such as the mean and standard deviation should agree.

Expected Descriptive Statistics Output

^a Multiple modes exist. SPSS reports the smallest tied value. Study hours have three tied modes: 8, 10, and 12. Every quiz score occurs once, so there is no useful unique mode; the displayed value 52 should not be described as a typical score.

Check one frequency table

The age frequency table should show that age 20 occurs four times, or 20% of the 20 cases. This confirms that 20 is the unique age mode.

The final row is condensed here for readability. SPSS displays a separate row for every observed age.

Interpret the SPSS Results

Age

The mean age is 22.60 years, the median is 22 years, and the most common age is 20 years. Ages span 18 to 30, giving a range of 12 years. The sample standard deviation is 3.283 years, so the ages typically vary by about 3.28 years around the mean. The positive skewness of 0.722 suggests some right-skew in this small sample, but one statistic alone does not establish a distributional model.

Weekly study time

The mean is 10.40 hours and the median is 10 hours. The sample standard deviation is 2.761 hours, and the observed values run from 6 to 16 hours. There is no single mode: 8, 10, and 12 each occur three times. If SPSS shows 8 with a footnote, report the tied modes rather than saying that 8 is the only typical value.

Quiz score

The average score is 70.50%, and half of the scores fall at or below 71%. The sample standard deviation is 10.425 percentage points, while the range is 37 points. Skewness is approximately zero (−0.003), which indicates little sample asymmetry. It does not prove that the population is normally distributed. Because each score occurs once, the mode adds no useful summary.

Example Results Paragraph

Data were available for all 20 fictional students. Participants had a mean age of 22.60 years (SD = 3.28, median = 22, range = 18–30). They studied an average of 10.40 hours per week (SD = 2.76, median = 10, range = 6–16) and earned a mean practice-quiz score of 70.50% (SD = 10.43, median = 71, range = 52–89). The quiz-score distribution showed little sample skewness (skewness = −0.003).

Common mistakes to avoid

1. Averaging an ID variable. Its numeric appearance does not make it a quantitative measurement.
2. Calling the smallest tied value the only mode. Read the SPSS footnote when multiple modes exist.
3. Confusing range with observed limits. The range is maximum minus minimum; report the limits separately when useful.
4. Calling the standard deviation an “average score.” The mean describes center; the standard deviation describes spread around the mean.
5. Claiming normality from skewness alone. Also inspect a histogram or Q–Q plot and consider the sample size and study design.
6. Interpreting description as causation. A table of means cannot establish that study time changed quiz performance.

Check the Numbers

Paste any one numeric column into the Statskan descriptive statistics calculator and compare its mean, median, sample standard deviation, variance, range, minimum, and maximum with the table above.

Open the Descriptive Statistics Calculator

Matching calculations verify the arithmetic for this dataset. You still need to choose meaningful variables and write an interpretation that fits the question.

Related SPSS Resources

• How to interpret SPSS output
• SPSS homework guidance
• Human statistics homework help
• Statskan Honor Code

Software reference: IBM explains the available Frequencies statistics, including mean, median, mode, standard deviation, range, and skewness.