The average is another name for the mean of a data set. To find the average, add all the numbers in the data set. Then divide by how many numbers there are.

• Data set: 3, 5, 6, 8, 11, 12
• \(3+5+6+8+11+12=45\)
• \(45 \div 6 = 7.5\)

The average is 7.5.

A box plot is a way to represent data on a number line with a box and some lines. The data is divided into four sections by 5 values. Those values are the minimum, first quartile, median, third quartile, and maximum.

A set of categorical data has values that are words instead of numbers.

For example, Han asks 5 friends to each name their favorite color. Their answers are “blue,” “blue,” “green,” “blue,” and “orange.”

The center of a data set is a value in the middle. It represents a typical value for the data set.

The center of this data set is between 4.5 and 5 kilograms. So a typical cat in this group weighs between 4.5 and 5 kilograms.

The distribution of a data set tells how many times each value occurs.

• In the data set blue, blue, green, blue, orange, the distribution is 3 blues, 1 green, and 1 orange.

• This dot plot shows the distribution for the data set 6, 10, 7, 35, 7, 36, 32, 10, 7, 35 kilograms.

  

A dot plot is a way to represent data with dots. Each dot above a number shows one time the value occurs in the set.

The interquartile range is one way to measure how spread out a data set is. To find the IQR, subtract the first quartile (Q1) from the third quartile (Q3).

For example, the IQR of this data set is 20 because \(50-30=20\).

The mean is one way to measure the center of a data set. It can be thought of as a balance point. To find the mean, add all the numbers in the data set. Then divide by how many numbers there are.

• Data set: 7, 9, 12, 13, 14
• Add values: \(7+9+12+13+14=55\)
• Divide by number of values: \(55 \div 5 = 11\)

The mean is 11. So, the typical travel time is 11 minutes.

The mean absolute deviation (MAD) is one way to measure how spread out a data set is. To find the MAD, find the distance between each data value and the mean. Add all the distances. Then divide by how many distances there are.

• Data set: 7, 9, 12, 13, 14
• Add distances: \(4+2+1+2+3=12\)
• Divide by number of distances: \(12 \div 5 = 2.4\)

The MAD is 2.4. So, these travel times are typically 2.4 minutes away from the mean of 11 minutes.

A measure of center is a value that seems typical for a data distribution.

Mean and median are both measures of center.

The median is one way to measure the center of a data set. It is the middle number when the data set is listed in order of value.

• For the data set 7, 9, 12, 13, 14, the median is 12.
• For the data set 3, 5, 6, 8, 11, 12, there are 2 numbers in the middle. The median is the average of these 2 numbers. \(6+8=14\), and \(14 \div 2 = 7\). The median is 7.

A set of numerical data has values that are numbers.

For example, Han lists the ages of people in his family: 7, 10, 12, 36, 40, 67.

Quartiles are the numbers that divide a data set into four sections. Each section has the same number of data values.

In this data set, the first quartile (Q1) is 30. The second quartile (Q2) is the median, 43. The third quartile (Q3) is 50.

The range is the distance between the smallest and largest values in a data set.

In the data set 3, 5, 6, 8, 11, 12, the range is 9, because \(12-3=9\).

The spread of a set of data tells how far apart the values are.

These dot plots show that the travel times for students in South Africa are more spread out than for students in New Zealand.

A statistical question can be answered by collecting data that has different values. Here are some examples of statistical questions:

• Who is the most popular musical artist at your school?
• When do students in your class typically eat dinner?
• Which classroom in your school has the most books?

The variability of a data set describes how different the values are.

Data set B has many different values, while data set A has more of the same values. So, data set B has more variability.