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.
Showing a random 20 of 50 problems.
Example 1
challenge
Prove that if every value lies within 2 of the mean, the range is at most 4.
Example 2
medium
Set {6,6,6,6,14}. Find the range. Is the spread large or small?
Example 3
easy
Low variability means values are __________ together.
Example 4
medium
Two boxes of cereal weigh 400,401,399,400 g vs 380,420,410,390 g. Which factory is more consistent?
Example 5
hard
Why do scientists report variability along with averages in experiments?
Example 6
easy
Which set has more variability: {5,5,5} or {1,5,9}?
Example 7
medium
After adding 5 to all data, what happens to variability?
Example 8
challenge
A set of five integers has range 0. What can you say about the data?
Example 9
challenge
Design two data sets of four numbers each that have the same mean of 10 but very different variability. Show both ranges.
Example 10
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 11
medium
A factory wants low variability in bolt length. Why not just track the mean length?
Example 12
easy
Plant heights: {4,4,5,5} cm or {1,4,5,9} cm. Which set has higher variability?
Example 13
easy
Daily temperatures: {72,73,74} or {60,73,86}. Which has higher variability?Daily temperatures (°F). Which set has higher variability?
Example 14
challenge
Two sets have equal range but different variability 'feel'. Construct sets where most B values cluster but A spreads evenly.
Example 15
easy
Does adding a far-away value increase variability?
Example 16
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 17
medium
Cookie weights from a bakery (g): 20,21,20,19,20. Find the range.
Example 18
medium
Sam's quiz scores: 7,8,8,9,8,7. Find the range.Sam's quiz scores. Find the range.
Example 19
medium
Set {3,5,7,9} vs {1,5,7,11}: same mean? Which is more variable?