Problem-Solving and Data Analysis · Math

One-variable data

One-variable data: mean, median, range, standard deviation as a concept, and how outliers affect each.

15 questions in the bank · 3 easier · 8 medium · 4 harder · this domain is ≈15% of the section

Learn it in the Guide

What to watch for

Sort before finding a median. The mean uses every value and is pulled hard by extremes; the median barely moves — that difference is what most of these questions are really testing.

How the question is worded

These are the actual stems used in the bank — the SAT reuses a small set of wordings, and recognising them saves time on test day.

  • The list shows 5 data values: 7, 12, 17, 22, 27. What is the mean of these values?
  • The list shows 6 data values: 8, 12, 15, 19, 23, 25. What is the mean of these values?
  • The list shows 6 data values: 6, 8, 12, 14, 16, 28. What is the mean of these values?
  • What is the median of the data set 3, 5, 17, 11, 37, 7?

Worked examples

easyThe list shows 5 data values: 7, 12, 17, 22, 27. What is the mean of these val…

The list shows 5 data values: 7, 12, 17, 22, 27. What is the mean of these values?

Answer: 17

Explanation

Add the values (7 + 12 + 17 + 22 + 27 = 85) and divide by how many there are (5): 85/5 = 17.

mediumWhat is the median of the data set 3, 5, 17, 11, 37, 7?

What is the median of the data set 3, 5, 17, 11, 37, 7?

  • A. 7
  • B. 9
  • C. 13
  • D. 14

Answer: B. 9

Explanation

Sort first: 3, 5, 7, 11, 17, 37. With 6 values, the median is the average of the middle two (7 and 11): 9. Forgetting to sort is the error the question is designed around.

hardA data set consists of the values 13, 18, 21, 23, 26. A new value, 66, is adde…

A data set consists of the values 13, 18, 21, 23, 26. A new value, 66, is added to the set. How does adding this value affect the mean and the median?

  • A. Neither the mean nor the median changes.
  • B. The median increases more than the mean.
  • C. The mean increases more than the median.
  • D. The mean and the median increase by the same amount.

Answer: C. The mean increases more than the median.

Explanation

The mean uses every value, so one large value (66) pulls it up substantially. The median only moves from the 3rd value (21) to the average of the 3rd and 4th (22) — a small shift. Extreme values stretch the mean; the median resists them.