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.

A chance experiment is something that can be done over and over again, and what will happen each time is not known.

For example, each time the spinner is spun, it could land on red, yellow, blue, or green.

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.

An event is a set of 1 or more outcomes in a chance experiment.

For example, if a number cube is rolled, there are 6 possible outcomes.

Some events are “rolling a number less than 3,” “rolling an even number,” or “rolling a 5.”

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.

An outcome of a chance experiment is one of the things that can happen.

For example, the possible outcomes of tossing a coin are heads and tails.

A population is a set of people or things that is studied.

For example, someone wants to study the heights of people on different sports teams. The population is all the people on all of the teams.

The probability of an event is a number that tells how likely it is to happen. A probability of 1 means the event will always happen. A probability of 0 means the event will never happen.

For example, the probability of selecting a moon block at random from this bag is \(\frac45\).

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.

An outcome of a chance experiment is random if it cannot be predicted. For example, the result of rolling a standard number cube is random because it could result in 1, 2, 3, 4, 5, or 6, and nobody can know which value it will be until it is rolled.

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 \(12-3=9\).

A sample is representative of a population if they match closely. They are very alike in shape, center, and spread.

This dot plot shows the distribution for a population.

A dot plot labeled dollars per pound of catfish. The numbers 1.6 through 2.8 in increments of zero point 2 are indicated. The data are as follows: 1 point 6 dollars per pound, 4 dots. 1 point 7 dollars per pound, 20 dots. 1 point 8 dollars per pound, 24 dots. 1 point 9 dollars per pound, 2 dots. 2 dollars per pound, 10 dots. 2 point 1 dollars per pound, 2 dots. 2 point 2 dollars per pound, 6 dots. 2 point 3 dollars per pound, 4 dots. 2 point 4 dollars per pound, 4 dots. 2 point 5 dollars per pound, 6 dots. 2 point 6 dollars per pound, 10 dots. 2 point 7 dollars per pound, 4 dots. 2 point 8 dollars per pound, 4 dots.

This dot plot shows the distribution of a sample that is representative of the population.​​​​​

A dot plot labeled dollars per pound of catfish. The numbers 1.6 through 2.8 in increments of zero point 2 are indicated. The data, titled Sample 1, are as follows: 1 point 6 dollars per pound, 1 dots. 1 point 7 dollars per pound, 4 dots. 1 point 8 dollars per pound, 5 dots. 2 dollars per pound, 2 dots. 2 point 2 dollars per pound, 2 dots. 2 point 4 dollars per pound, 1 dot. 2 point 5 dollars per pound, 2 dots. 2 point 6 dollars per pound, 2 dots. 2 point 7 dollars per pound, 1 dot. 2 point 8 dollars per pound, 1 dot

A sample is part of a population. For example, a population could be all the seventh grade students at one school. One sample of that population is all the seventh grade students who are in band.

The sample space is the list of every possible outcome for a chance experiment.

For example, the sample space for tossing two coins is:

A simulation is an experiment that is used to estimate the probability of a real-world event.

Suppose the weather forecast says there is a 25% chance of rain. This situation can be simulated with a spinner that has four equal sections. If the spinner stops on red, it represents rain. If the spinner stops on any other color, it represents no rain.

A circular spinner divided into 4 equal parts. The top left section is red and labeled “R.” The top right section is blue and labeled “B.” The bottom right section is green and labeled “G.” The bottom left section is yellow and labeled “Y.” The spinner dial points to the section labeled "G."

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.