Practice Spread vs Center in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick 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.

Showing a random 20 of 50 problems.

Example 1

easy
True or false: two data sets with equal means must look identical.

Example 2

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 3

medium
Two basketball players average 2020 points/game. Player A scores between 1818 and 2222; Player B scores between 00 and 4040. Which is more reliable?

Example 4

easy
Set A: 29,30,3129,30,31. Set B: 10,30,5010,30,50. Same center?

Example 5

easy
Set A: 29,30,3129,30,31. Set B: 10,30,5010,30,50. Which has more spread?

Example 6

medium
A weather report says 'average high this week is 75 degrees.' What is missing?

Example 7

easy
Which describes 'how scattered': center or spread?

Example 8

easy
Bus A arrives in 15±115\pm 1 min; Bus B arrives in 15±1215\pm 12 min. Which is more predictable?

Example 9

easy
Quiz scores: Class A all 8080; Class B has scores from 6060 to 100100. Which has zero spread?

Example 10

easy
Which question does 'center' answer: 'where is the middle' or 'how scattered'?

Example 11

medium
If you multiply every value by 22, what happens to the center and the spread?

Example 12

easy
Two delivery services average 3030 min; A ranges 2828-3232, B ranges 1010-5050. Which is more reliable?

Example 13

hard
Pizza shop A delivers in 25±325\pm 3 min; shop B delivers in 30±130\pm 1 min. You need food in 32 minutes. Which is the safer bet?

Example 14

easy
Set A: 99,100,10199, 100, 101. Set B: 50,100,15050, 100, 150. Which has more spread?

Example 15

medium
Two stocks both gain 5%5\% a year on average. Stock A swings ±1%\pm 1\%; Stock B swings ±30%\pm 30\%. Which is riskier?

Example 16

medium
A team's daily commutes (min): 30,31,30,29,3030, 31, 30, 29, 30. Median commute is 3030. What does the small spread imply?

Example 17

medium
Set A: {50,50,50}\{50,50,50\}, Set B: {0,50,100}\{0,50,100\}. Compare center and spread.

Example 18

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 19

medium
Data has center 5050 and large spread. Adding 1010 to every value, what changes?

Example 20

medium
Two dartboards: thrower A's darts land {9,10,11}\{9,10,11\}, thrower B's land {0,10,20}\{0,10,20\}. Both 'aim' is the bullseye (center 10). Compare.