Chapter 10 of 10

Statistics & Data

How can a collection of values tell a clear story?

Statistics begins with questions that expect variability. Data displays reveal shape, center, and spread, while numerical measures summarize a distribution. A good description connects those features back to the original context.

The big ideas

Understand these before you worry about speed.

Statistical questions anticipate variation

A statistical question is answered by collecting data and expects more than one value. A question about a single fixed fact is not statistical.

Example“How many minutes do students in our class read each night?” is statistical.

Mean and median describe center differently

The mean shares the total equally across all values. The median is the middle ordered value and is less affected by an extreme value.

ExampleFor

\displaystyle 2,3,4,5,16

, the mean is

\displaystyle 6

but the median is

\displaystyle 4

Range and IQR describe spread

Range subtracts the minimum from the maximum. Interquartile range subtracts the first quartile from the third and describes the middle half of the data.

ExampleIf

\displaystyle Q_1=8

and

\displaystyle Q_3=15

, then

\displaystyle \operatorname{IQR}=15-8=7

Choose a display that fits the data

Dot plots preserve individual values, histograms group numerical intervals, and box plots emphasize quartiles and overall spread. Always read the title, labels, units, and scale.

ExampleA histogram is useful for seeing the shape of a large set of test scores.

Worked example

Follow the reason for each step—not just the symbols.

Problem

Describe the center and spread of $\displaystyle 4,5,5,6,10$ .

The data are already ordered. The middle value is the median: $\displaystyle 5$ .
Add and divide by $\displaystyle 5$ to find the mean: $\displaystyle \frac{4+5+5+6+10}{5}=6$ .
Find the range: $\displaystyle 10-4=6$ .
The high value 10 pulls the mean above the median, suggesting a right-side stretch.

AnswerMean $\displaystyle 6$ , median $\displaystyle 5$ , range $\displaystyle 6$

Try it yourself

Work on paper first. Open each answer only when you are ready to check.

Is “How old is the principal?” a statistical question?

Check answer

No; it asks for one fixed value.

Find the mean of $\displaystyle 6,8,8,9,14$ .

Check answer

$\displaystyle 9$

Find the median and range of $\displaystyle 3,4,7,7,12,15$ .

Check answer

Median $\displaystyle 7$ ; range $\displaystyle 12$

For a data set with $\displaystyle Q_1=11$ and $\displaystyle Q_3=19$ , find the IQR.

Check answer

$\displaystyle 8$

Practice and tools

Use the resource that matches what you need next.

Worksheet

Statistics & Data

The big ideas

Statistical questions anticipate variation

Mean and median describe center differently

Range and IQR describe spread

Choose a display that fits the data

Worked example

Describe the center and spread of $\displaystyle 4,5,5,6,10$ .

Try it yourself

Practice and tools

Statistics & Mean/Median/Mode

Probability Basics

6th Grade Math Final Test

Statistical questions anticipate variation

Mean and median describe center differently

Range and IQR describe spread

Choose a display that fits the data

Describe the center and spread of 4,5,5,6,10\displaystyle 4,5,5,6,104,5,5,6,10.

Statistics & Mean/Median/Mode

Probability Basics

6th Grade Math Final Test

Describe the center and spread of $\displaystyle 4,5,5,6,10$ .