Perfect1600

Digital SAT · Solve it in Desmos

How to Solve Mean, Median, and Range on Desmos (Digital SAT)

A Desmos list shines on long data and on added-or-removed-value questions, since it recomputes at once. For a short list you can work by hand, but the list removes counting and summing errors.

Perfect1600 Content Team·Uses the same Desmos calculator that is built into the Digital SAT

Full method for mean, median, and range

The Desmos steps

  1. 1

    Enter the data as a list

    Type it in Desmos, like D = [4, 7, 7, 9, 12, 15, 18].

  2. 2

    Use the built-in functions

    Type mean(D) or median(D) for the value, with no hand arithmetic.

  3. 3

    Edit for changes

    Add or remove a value in the list and read the new statistic instantly.

Open a real question in the same Desmos calculator you get on Perfect1600, with the setup already typed in:

Worked in Desmos

Medium example

A data set of 6 numbers has a mean of 15.

If the number 9 is removed from the data set, what is the mean of the remaining 5 numbers?
A
15
B
15.5
16.2
D
17

A: Incorrect. This is the original mean, ignoring the removal.

B: Incorrect. This results from dividing the new sum by 6 instead of 5.

C: Correct. The original sum is 6×15=906 \times 15 = 90; removing 9 gives 8181, and 81÷5=16.281 \div 5 = 16.2.

D: Incorrect. This results from subtracting too much from the original sum.

Explanation

New mean =90−95=16.2= \frac{90 - 9}{5} = 16.2.

Detailed explanation

The original sum is 6×15=906 \times 15 = 90; removing 9 leaves a sum of 81 over 5 values, so the mean is 81÷5=16.281 \div 5 = 16.2.

Medium example

The data set 5, 8, 8, 11, and 18 has its largest value increased by 10.

By how much does the mean of the data set increase?
2
B
5
C
8
D
10

A: Correct. The total increases by 10 spread over 5 values, so the mean increases by 10÷5=210 \div 5 = 2.

B: Incorrect. This divides the increase by 2 rather than by the 5 values.

C: Incorrect. This is unrelated to spreading the increase across the values.

D: Incorrect. This is the increase in the total, not the increase in the mean.

Explanation

Mean increase =105=2= \frac{10}{5} = 2.

Detailed explanation

Adding 10 to one value raises the sum by 10, and dividing that change across the 5 values increases the mean by 10÷5=210 \div 5 = 2.

Hard example
A data set consists of the values 4, 7, 7, 9, 12, 15, and 18. What is the median of the data set?
A
77
99
C
1010
D
1212

A: Incorrect. 7 is the mode, not the middle value.

B: Correct. With 7 values in order, the median is the 4th value, which is 9.

C: Incorrect. 10 is the mean, not the median.

D: Incorrect. 12 is the 5th value, not the middle.

Explanation

7 ordered values; the 4th (middle) is 9.

Try it with the calculator

Question 1easy
Data figure
34567891011Value

What is the mean of the data set 4, 7, 9, and 10?

Question 2easy
Data figure
2345678910Value

What is the median of the data set 3, 5, 5, 8, and 9?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

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Desmos questions

Can Desmos solve mean, median, and range questions on the SAT?

A Desmos list shines on long data and on added-or-removed-value questions, since it recomputes at once. For a short list you can work by hand, but the list removes counting and summing errors.

Is the Desmos calculator really built into the Digital SAT?

Yes. The Bluebook testing app includes the Desmos graphing calculator on every Math question, so the method here is one you can use on test day, not a workaround.

Should I still learn the algebra?

Yes. Desmos is fastest when you know what to type and what to read. Learn the underlying method on the full guide, then use the calculator to move quickly and to check your work.

Master mean, median, and range, calculator and all

Every Digital SAT question type comes with the method, the Desmos shortcut, and free practice with instant feedback.

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