SAT Math: One-variable data: center and spread

One-variable data: centre and spread.

Problem-Solving and Data Analysis · One-variable data: distributions and measures of center and spread
Both modules
12 practice questions · 3 with free solutions
Calculator allowed (Desmos)

Practise one-variable data: center and spread →Adaptive SAT module

What the test covers

Mean, median, range, standard deviation (qualitative)
Effect of adding or removing a value

Key ideas

Mean = total $\div$ count. If one value is removed, subtract it from the total.
Median: middle value of the ordered data (mean of the two middle values when the count is even).
An outlier moves the mean much more than the median; range and standard deviation measure spread.

Common mistakes

Order the data before finding the median.
Adding a large value can change the median as well as the mean.

Do it in Desmos

Enter the list as L = [ ... ] and use mean(L), median(L), stdev(L).

IB link: IB SL 4.2-4.3.

Worked example

The data set 4, 7, 7, 9, 13 has one value, 25, added to it. Which statement about the new data set is true?

The mean and median increase by the same amount.
The mean and median do not change.
The median increases by more than the mean does.
The mean increases by more than the median does.

Answer: D: The mean increases by more than the median does.

Old mean $40 / 5 = 8$ , old median 7. New mean $65 / 6 \approx 10.83$ (up about 2.83); new median $\frac{7 + 9}{2} = 8$ (up 1). The mean increases by more.

Practice questions

Try each question before opening the solution. Desmos or your own calculator is allowed on every SAT Math question. Solutions to the first 2 are open to everyone; the rest need only a free account. Every answer here was checked independently before it was published.

Question 1

The mean of 5 numbers is 20. When one of the numbers is removed, the mean of the remaining 4 numbers is 21. What number was removed?

Student-produced response: type your answer.

Show the answer and solution

Answer: 16

Total before: $5 \times 20 = 100$ . Total after: $4 \times 21 = 84$ . Removed: $16$ .

Question 2

The data set $6, 8, 9, 16, 17$ has one value, 50, added to it. Which statement about the new data set is true?

The median increases by more than the mean does.
The mean increases by more than the median does.
The mean and median do not change.
The mean and median increase by the same amount.

Show the answer and solution

Answer: B: The mean increases by more than the median does.

Old mean $56 / 5 = 11.2$ , old median $9$ . New mean $106 / 6 \approx 17.67$ ; new median $\frac{9 + 16}{2} = 12.5$ . The mean increases by more than the median does.

Question 3

The mean of six numbers is 12. When one of the numbers is removed, the mean of the remaining five numbers is 11. What number was removed?

Student-produced response: type your answer.