Range — Grade 8 Math, what it means and where it is taught

The set of outputs that actually occur.

Taught in Grade 8 Math.

Where it is taught

What uses it later

This idea is needed for:

Practise this idea

14 questions in the course bank use Range, in Solving Inequalities, What Is a Function?, Lines of Best Fit, Bivariate Data & Correlation, Statistics: Centre, Spread & Displays, Sampling, Simulation & Inference. The first 8 are below; the rest are in those units.

Problem 1

How many integers satisfy -7 ≤ 2x - 1 < 9?

Worked answer

8

Add 1 everywhere: -6 ≤ 2x < 10

Divide by 2: -3 ≤ x < 5

Integers: -3, -2, -1, 0, 1, 2, 3, 4

That is 8 values — note 5 is excluded.

Problem 2

For f(x) = x2 with domain {-2, -1, 0, 1, 2}, list the range.

Worked answer

{0, 1, 4}

4, 1, 0, 1, 4

Distinct values: 0, 1, 4

Problem 3

Data covers x from 2 to 15. Predicting at x = 80 is

  1. extrapolation, and unsafe
  2. interpolation, and safe
  3. impossible to compute
  4. the same as the mean
Worked answer

extrapolation, and unsafe

80 is far outside 2 to 15

That is extrapolation

The pattern may not continue

Problem 4

A best-fit line for a child's height against age gives y = 2.4x + 30 inches. Predict the height at age 40 and say whether to trust it.

Worked answer

126 inches, not trustworthy

2.4(40) + 30 = 126 inches

That is over 10 feet

Far outside the data range, so an unsafe extrapolation

Problem 5

A regression on data for x between 5 and 20 gives y = 3x + 10. Is predicting at x = 200 reliable? Answer yes or no.

Worked answer

no

200 is far outside 5 to 20

That is extrapolation

So not reliable

Problem 6

Find the range of 12, 5, 20, 9.

Worked answer

15

20 - 5 = 15

Problem 7

Which pair of statistics is resistant to outliers?

  1. Median and IQR
  2. Mean and standard deviation
  3. Mean and range
  4. Median and range
Worked answer

Median and IQR

Median ignores the extremes

IQR uses only the middle half

Mean, range and standard deviation all move a lot

Problem 8

A poll gives 52% with margin 3%. Can a lead be claimed?

  1. No — the interval includes 50%
  2. Yes — 52 is above 50
  3. Yes — the margin is small
  4. Not enough information
Worked answer

No — the interval includes 50%

The range is 49% to 55%

It contains 50%, so the data has not decided

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