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What College Really Costs: Net Price by Family Income

Students compare what families in five income brackets actually pay after grants at 1,051 colleges, summarize each distribution, and estimate the mean gap between the highest and lowest bracket with paired differences.

AP StatisticsUnit 1: Exploring One-Variable Data; Unit 7: Inference for Quantitative Data: Means
TimeOne to two 50-minute class periods
Common CoreHSS.ID.A.1, HSS.ID.A.2, HSS.ID.A.3, HSS.IC.B.4
DataCSV, 1,051 rows

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Learning objectives

  • Summarize and compare distributions with five-number summaries and boxplots.
  • Explain why the median can be a better summary of center than the mean for skewed data.
  • Recognize paired data and analyze the differences as one sample.
  • Construct and interpret a one-sample t interval for a mean difference.

Materials

  • The lesson CSV (one row per college, one column per income bracket)
  • A graphing calculator or spreadsheet
  • The student worksheet below

CSV: https://collegecalcai.com/api/data-csv/teach/net-price-by-family-income

About the data: Average net price (cost of attendance minus grants and scholarships) for students receiving federal aid, by family income: College Scorecard, release 2026-06-10. Colleges reporting all five brackets. Brackets: net_price_0_30k = $0 to $30,000; net_price_30_48k = $30,001 to $48,000; net_price_48_75k = $48,001 to $75,000; net_price_75_110k = $75,001 to $110,000; net_price_110k_plus = Over $110,000. The class sample of 30 colleges was drawn at random with a fixed seed.

Columns: college, state, type, net_price_0_30k, net_price_30_48k, net_price_48_75k, net_price_75_110k, net_price_110k_plus, in_class_sample.

Student worksheet

Name: ______________________ Period: ______ Open the CSV in a spreadsheet, a graphing calculator or statistics software.

  1. Find the five-number summary of net_price_0_30k and of net_price_110k_plus. Make side-by-side boxplots of the five income brackets.
  2. For net_price_0_30k, compare the mean and the median. What does the comparison suggest about the shape of the distribution?
  3. How many of the colleges have an average net price under $10,000 for families earning $30,000 or less? What share is that?
  4. Why are net_price_0_30k and net_price_110k_plus for the same college paired data? Compute the difference (110k_plus minus 0_30k) for every college, and give its mean and standard deviation.
  5. Using only the rows with in_class_sample = 1 (a random sample of 30), construct and interpret a 95% t interval for the mean difference.
  6. Does your interval capture the mean difference across all colleges from question 4? Should it, every time?

Teacher key

Every value below is computed by code from the same CSV students download.

  1. $0 to $30,000: min -$3,012, Q1 $10,029, median $13,951, Q3 $19,481, max $50,560. Over $110,000: min $3,054, Q1 $20,328, median $25,439, Q3 $31,967, max $80,192. Medians by bracket, lowest to highest income: $13,951, $14,372, $16,883, $20,735, $25,439. (Quartiles by the TI-84 method; software may differ slightly.) A negative value means grants exceeded the cost of attendance on average.
  2. Mean $14,979, median $13,951. The mean is greater than the median, which suggests a distribution skewed to the right: a few colleges charge low-income families much more than most do.
  3. 260 of 1,051 colleges, or 24.7%.
  4. Each college gives both values, so the two numbers are linked by college. Difference: mean $12,602, standard deviation $10,024 (n = 1,051).
  5. Sample of 30: mean difference $11,974, s = $5,943, t* = 2.045 with 29 df, margin of error $2,219. Interval: ($9,755, $14,193). We are 95% confident that the interval from $9,755 to $14,193 captures the true mean difference in net price between the highest and lowest income brackets at these colleges. Conditions: random sample; 30 is less than 10% of 1,051; n = 30 only just meets the guideline of 30, so also check a dot plot of the differences for strong skew or outliers.
  6. The mean difference across all colleges is $12,602. The class interval captures it. Not every time: about 95% of intervals built this way capture the true mean.

Extension

  • Compare the paired differences for public and private colleges. Which type shows the larger gap between income brackets, and why might that be?
  • Look up a college's net price calculator and compare its estimate for your family with the bracket average in the file.

All free lessons

Free to use and share (CC BY 4.0). Source: CollegeCalcAI, collegecalcai.com/teach/net-price-by-family-income, from U.S. Department of Education data (IPEDS and the College Scorecard). Unit names follow the College Board AP Statistics Course and Exam Description; not endorsed by the College Board.