Data Variability Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Data Variability.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

Data variability describes how much the values in a data set are spread out or clustered together around the center. High variability means values are widely scattered; low variability means they are tightly grouped near the average.

Two archery targets both have average hits at the bullseye. But one archer's arrows are scattered all over, while the other's are clustered tightly. Same average, very different consistency. That difference is variability.

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How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Data Variability asks how tightly or loosely the values sit around the data set, not just where the middle is.

Common stuck point: Students often know a procedure related to data variability but skip the recognition step: Do I need to describe how far the data values extend or vary, rather than where the middle is? That leads to a calculation or graph that looks reasonable but answers a different question.

Sense of Study hint: Ask: Do I need to describe how far the data values extend or vary, rather than where the middle is?

Worked Examples

Example 1

medium

Jenny times her morning run:

25, 26, 25, 24, 25

minutes. Pat's times are

20, 30, 22, 28, 25

. Whose runs are more consistent?

Answer

\text{Jenny}

First step

Jenny's range:

26-24=2

minutes.

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Example 2

medium

Heights of seedlings in two gardens: A:

\{10, 11, 9, 10, 10\}

; B:

\{6, 14, 8, 12, 10\}

. Compare variability.

Seedling heights (cm). Which garden has lower variability?

Example 3

medium

Test scores in two classes have the same mean of

80

. Class A:

\{78,80,82\}

. Class B:

\{60,80,100\}

. Find each range and compare.

Test scores, both classes mean 80. Find each range and compare.

Example 4

hard

Game scores:

\{8, 9, 10, 11, 12\}

and

\{10, 10, 10, 10, 10\}

. Compare mean and variability.

Example 5

hard

Rainfall in city X (in cm) for 5 weeks:

2, 2, 3, 3, 10

. Find the range. Why might a meteorologist mention both the median and the range?

Rainfall in city X (cm). Find the range. Why report both median and range?

Example 6

challenge

Design two data sets of four numbers each that have the same mean of

10

but very different variability. Show both ranges.

Example 7

easy

Two classes took the same test. Class A scores: 70, 72, 68, 71, 69. Class B scores: 50, 90, 60, 80, 70. Both have a mean of 70. Which class has more variability?

Example 8

medium

Daily temperatures (°C) for a week: 20, 22, 19, 21, 20, 23, 21. Calculate the mean and describe the variability informally.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Which set has more variability:

\{5,5,5\}

\{1,5,9\}

Example 2

easy

What is the variability of

\{7,7,7,7\}

Example 3

easy

High variability means data is tightly grouped. True or false?

Example 4

easy

Two archers hit the same average spot. One clusters tightly. Which has lower variability?

Example 5

easy

Does adding a far-away value increase variability?

Example 6

easy

Which is a measure of variability: mean or range?

Example 7

easy

If all test scores are

90

, what is the variability?

Example 8

easy

Which set is more consistent: range

3

or range

30

Example 9

medium

Set A:

\{48,50,52\}

, Set B:

\{20,50,80\}

. Both mean

50

. Which has higher variability and why?

Both sets have mean 50. Which has higher variability?

Example 10

medium

Machine A makes parts

9.9,10.0,10.1

cm; Machine B makes

8,10,12

cm. Target is

10

. Which machine is more reliable?

Target length is 10 cm. Which machine is more reliable?

Example 11

medium

Why report variability alongside the mean of rainfall?

Example 12

medium

Set

\{2,4,6,8\}

\{1,4,6,9\}

: same mean? Which is more variable?

Example 13

medium

After multiplying all data by

3

, what happens to variability?

Example 14

medium

After adding

5

to all data, what happens to variability?

Example 15

medium

Which has more variability: daily temps in a desert (

40

5

) or a coast (

18

24

Example 16

challenge

Two sets have equal range but different variability 'feel'. Construct sets where most B values cluster but A spreads evenly.

Example 17

challenge

Prove that if every value lies within

2

of the mean, the range is at most

4

Example 18

challenge

Adding the mean as a new value: does variability go up, down, or stay? Argue with MAD intuition.

Example 19

medium

Set

\{3,5,7,9\}

\{1,5,7,11\}

: same mean? Which is more variable?

Example 20

medium

A factory wants low variability in bolt length. Why not just track the mean length?

Example 21

easy

Which set has more variability:

\{10, 10, 10\}

\{2, 10, 18\}

Example 22

easy

Two pencils measure

7

and

7

inches. What is the variability?

Example 23

easy

Plant heights:

\{4, 4, 5, 5\}

cm or

\{1, 4, 5, 9\}

cm. Which set has higher variability?

Example 24

easy

Daily temperatures:

\{72, 73, 74\}

\{60, 73, 86\}

. Which has higher variability?

Daily temperatures (°F). Which set has higher variability?

Example 25

easy

Heights of three kids:

48, 50, 52

inches. Find the range.

Heights of three kids (inches). Find the range.

Example 26

medium

Two boxes of cereal weigh

400, 401, 399, 400

g vs

380, 420, 410, 390

g. Which factory is more consistent?

Example 27

medium

Set

\{6, 6, 6, 6, 14\}

. Find the range. Is the spread large or small?

Example 28

medium

If you add the same constant

c

to every value in a set, what happens to the variability?

Example 29

medium

Sam's quiz scores:

7, 8, 8, 9, 8, 7

. Find the range.

Sam's quiz scores. Find the range.

Example 30

medium

Cookie weights from a bakery (g):

20, 21, 20, 19, 20

. Find the range.

Example 31

medium

Why might a teacher prefer a homework score with low variability across the class?

Example 32

hard

Five dice rolls:

1, 1, 6, 6, 1

. Find the range and describe the variability.

Example 33

hard

A class has scores all between

90

and

100

except for one

0

. Does the range give a fair picture of typical variability?

Example 34

hard

If you double every value in a data set, what happens to the range?

Example 35

hard

Why do scientists report variability along with averages in experiments?

Example 36

challenge

A set of five integers has range

0

. What can you say about the data?

Example 37

easy

Set X: {5, 5, 5, 5, 5}. Set Y: {1, 3, 5, 7, 9}. Both have mean 5. Which set has zero variability and why?

Example 38

easy

Team A scores 14, 15, 15, 16, 15 in five games. Team B scores 10, 15, 20, 15, 15. Which team has greater variability? Explain briefly.

← Back to Data Variability Practice Mode

Related Concepts

Mean as Fair Share Range Standard Deviation

Background Knowledge

These ideas may be useful before you work through the harder examples.

mean fair share