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

A dot far away from the rest of the pattern.

Taught in Grade 8 Math.

Where it is taught

Practise this idea

11 questions in the course bank use Outlier, in Sampling, Inferences & Comparing Populations, Scatter Plots & Association, Bivariate Data & Correlation, Statistics: Centre, Spread & Displays, Statistical Questions & Distributions. The first 8 are below; the rest are in those units.

Problem 1

A data set is 12, 15, 15, 18, 140. Which measure better describes a typical value?

  1. The mean
  2. The median
  3. They are equally good
Worked answer

The median

Mean = 2005 = 40

Median = 15

No value is near 40 — the outlier 140 dragged the mean away from the data.

Problem 2

On a plot of height against weight, one point is far above the pattern. It is

  1. an outlier
  2. a cluster
  3. the median
  4. impossible
Worked answer

an outlier

It does not follow the trend of the rest

So it is an outlier

Problem 3

A point at the far right of a scatter plot lies exactly on the pattern. It is

  1. not an outlier
  2. an outlier
  3. the mean
  4. a cluster
Worked answer

not an outlier

This point follows the trend

So it is not an outlier, however extreme its x value

Problem 4

A plot of hours of television against grade shows a moderate negative linear association with two outliers. Write one sentence a statistician would accept about cause.

Worked answer

no cause can be concluded from this association

The data shows an association only

A third factor could drive both

So no causal claim is justified

Problem 5

A residual plot shows a clear curved arch. This means

  1. a line is the wrong model
  2. the line fits perfectly
  3. r must be zero
  4. the data has no outliers
Worked answer

a line is the wrong model

Structure in the residuals means the model missed something

A curve needs a curved model

Problem 6

Data: 20, 22, 24, 25, 400. Should you report the mean or the median?

Worked answer

median

400 is far from the rest

It drags the mean up to 98.2

The median, 24, is representative

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

Using the 1.5 × IQR rule with Q1 = 20 and Q3 = 32, is 55 an outlier? Answer yes or no.

Worked answer

yes

IQR = 12

1.5 × 12 = 18

Upper fence = 32 + 18 = 50

55 > 50, so yes

Elsewhere

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