Spread vs Center Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Spread vs Center.

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

Concept Recap

Center describes where the 'middle' of data lies; spread describes how far data extends from that center.

Two pizza delivery services both average 30-minute delivery (same center). But Service A ranges 28-32 minutes, while Service B ranges 10-50 minutes. Same center, wildly different spread. You'd trust A for consistent timing.

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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: Spread vs Center 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 spread vs center 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

Set A:

\{18, 20, 22\}

. Set B:

\{10, 20, 30\}

. Compute the means and ranges of each set.

Set A: {18, 20, 22} vs Set B: {10, 20, 30}

Answer

\text{means} = 20,\ \text{ranges} = 4, 20

First step

Mean of A

=(18+20+22)/3=20

; mean of B

=(10+20+30)/3=20

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Example 2

medium

Two students score

70, 80, 90

50, 80, 110

on three quizzes. Compare center and spread.

Quiz scores: {70, 80, 90} vs {50, 80, 110}

Example 3

medium

Two dartboards: thrower A's darts land

\{9,10,11\}

, thrower B's land

\{0,10,20\}

. Both 'aim' is the bullseye (center 10). Compare.

Dart landing distance from bullseye (cm): center = 10 for both

Example 4

hard

Pizza shop A delivers in

25\pm 3

min; shop B delivers in

30\pm 1

min. You need food in 32 minutes. Which is the safer bet?

Example 5

challenge

A hospital claims 'average wait is 8 minutes.' Patient stories report waits of 30+ minutes. Reconcile.

Example 6

medium

Two machines fill bottles. Machine A fills: 500, 502, 498, 501, 499 mL. Machine B fills: 490, 510, 480, 520, 500 mL. Both have a mean of 500 mL. Which machine is more reliable?

Example 7

medium

Dataset A: {10, 10, 10, 10, 10}. Dataset B: {2, 6, 10, 14, 18}. Compare their centres and spreads.

Practice Problems

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

Example 1

easy

Two sets have the same mean. What else should you compare?

Example 2

easy

Set A:

29,30,31

. Set B:

10,30,50

. Same center?

Set A: {29, 30, 31} vs Set B: {10, 30, 50}

Example 3

easy

Set A:

29,30,31

. Set B:

10,30,50

. Which has more spread?

Example 4

easy

Does a single mean tell you how consistent data is?

Example 5

easy

Two delivery services average

30

min; A ranges

28

32

, B ranges

10

50

. Which is more reliable?

Delivery time (minutes): both average 30 min

Example 6

easy

Which describes 'where the middle is': center or spread?

Example 7

easy

Which describes 'how scattered': center or spread?

Example 8

easy

Two classes both average

75

. Class A range

5

, Class B range

40

. Same scores?

Example 9

medium

Set A:

\{50,50,50\}

, Set B:

\{0,50,100\}

. Compare center and spread.

Set A: {50, 50, 50} vs Set B: {0, 50, 100}

Example 10

medium

A report says 'average wait is 5 min'. Why might that be misleading?

Example 11

medium

Set A spread is larger than B's, but both share the median. Which has values farther from the median more often?

Example 12

medium

Two archers both average a bullseye. One scatters, one clusters. Which has lower spread?

Example 13

medium

Given mean

20

for both, A has range

4

and B has range

40

. Which would you bet is more predictable next value?

Example 14

medium

Data has center

50

and large spread. Adding

10

to every value, what changes?

Example 15

medium

If every value is multiplied by

2

, how do center and spread change?

Example 16

challenge

Two data sets have equal mean and equal range but different MAD. Construct an example.

Example 17

challenge

Prove that two data sets with the same values in different order have identical center and spread.

Example 18

challenge

Set has mean

\mu

and all values within

d

\mu

. Show the range is at most

2d

Example 19

medium

Set A:

\{18,20,22\}

, Set B:

\{5,20,35\}

. Same mean? Which has more spread?

Set A: {18, 20, 22} vs Set B: {5, 20, 35}

Example 20

medium

A weather app reports only the average high. What spread info is missing for planning?

Example 21

easy

Set A:

99, 100, 101

. Set B:

50, 100, 150

. Same center?

Set A: {99, 100, 101} vs Set B: {50, 100, 150}

Example 22

easy

Set A:

99, 100, 101

. Set B:

50, 100, 150

. Which has more spread?

Example 23

easy

Quiz scores: Class A all

80

; Class B has scores from

60

100

. Which has zero spread?

Example 24

easy

Bus A arrives in

15\pm 1

min; Bus B arrives in

15\pm 12

min. Same center?

Arrival time (minutes): Bus A ±1 min vs Bus B ±12 min

Example 25

easy

Bus A arrives in

15\pm 1

min; Bus B arrives in

15\pm 12

min. Which is more predictable?

Example 26

medium

A factory wants parts close to 5 cm. Which is the bigger problem: mean drift or large spread?

Example 27

medium

A team's daily commutes (min):

30, 31, 30, 29, 30

. Median commute is

30

. What does the small spread imply?

Example 28

medium

If you add

5

to every value in a data set, what happens to the center and the spread?

Example 29

medium

If you multiply every value by

2

, what happens to the center and the spread?

Example 30

medium

Two stocks both gain

5\%

a year on average. Stock A swings

\pm 1\%

; Stock B swings

\pm 30\%

. Which is riskier?

Example 31

medium

Two basketball players average

20

points/game. Player A scores between

18

and

22

; Player B scores between

0

and

40

. Which is more reliable?

Points per game: both average 20 pts/game

Example 32

hard

True or false: it is possible for one data set to have a larger mean but a smaller spread than another. Give an example.

Example 33

hard

A data set's range is reported as

0

. What must be true about every value?

Example 34

hard

Heights of seedlings:

\{8,10,12\}

cm. After watering, all become

\{12,15,18\}

cm. How did center and spread change?

Seedling heights (cm): before {8, 10, 12} vs after {12, 15, 18}

Example 35

hard

Data

\{2, 4, 6, 8, 10\}

versus

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

. Compare center and spread.

Set A: {2, 4, 6, 8, 10} vs Set B: {6, 6, 6, 6, 6}

Example 36

challenge

Two data sets have means

50

and

60

and ranges

4

and

40

. Which is more reliable, and is it the one with the larger center?

Example 37

medium

A restaurant's lunch wait times (minutes) — Week 1: 5, 6, 5, 7, 5. Week 2: 3, 10, 4, 8, 3. Find the mean and range for each week and explain which week had more predictable service.

Example 38

medium

Two classes both have median score 75. Class A scores are 72, 74, 75, 76, 78. Class B scores are 60, 70, 75, 80, 90. Which class has greater spread, and which class seems more consistent?

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Related Concepts

Mean as Fair Share Data Variability Standard Deviation Interquartile Range (IQR)

Background Knowledge

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

mean fair sharevariability intro