In this chapter you will learn to:
- Collect and represent data on a number line, and in graphs, tables, and charts.
- Read and interpret data.
- Find the mode, median, and range of data.
- Identify clumps, holes, and outliers.
- Determine all possible outcomes of a situation.
- Solve problems by making a table.
- Statistics is a type of mathematics used to collect, organize, and display data for people to understand. Data are facts or information about people or things.
- A survey is a way to collect data or information that answers a question. You can use a tally chart or frequency table to record data.
- Line graphs show increases and decreases in a trend.
- Line plots are a portion of a number line used as a quick way to organize and represent data as it is collected.
- A clump is a group of data pieces on the graph. The clump of the line plot is 0 – 4.
- A hole is a place where there are no data pieces. The holes are at 5, 7, 9, 11, 12 and 15.
- Outliers are pieces of data that are much larger or smaller than the rest of the data. The outliers are 13 or 14.
- The mean is the total of the numbers divided by how many numbers there are.
1. Add up all the numbers: 7+ 9 + 11 + 6 + 13 + 6 + 6 + 3 + 11 = 72
2. Divide the answer by how many numbers there are: 72 divided by 9 = 8.
3. The mean is 8.
- The median is the middle value.
1. Put the numbers in order: 3 6 6 6 7 9 11 11 13
2. The number in the middle of the list is the median: 7.
3. If there are two middle values, the median is halfway between them:
3 6 6 6 7 8 9 11 11 13 – The median is 7.5
- The mode is the value that appears the most.
1. Put the numbers in order: 3 6 6 6 7 9 11 11 13
2. Look for the number that appears the most: 6.
- The range is the difference between the biggest and the smallest number.
1. Put the numbers in order: 3 6 6 6 7 9 11 11 13
2. Subtract the smallest number from the biggest number: 13 – 3 = 10
3. The range is 10.
Ratio and Probability
- Ratios are one way to compare 2 amounts. Ratios can be written in three forms: as words, as numbers with a colon separating the two amounts, and as fractions. For example: if a class has 14 boys and 15 girls, the ratio of boys to girls is 14 to 15, 14:15, or 14/15.
- The order of the numbers in the ratio is very important. For example, a class has 14 boys and 15 girls. If we are comparing girls to boys, the ratio is 15 to 14. If we are comparing boys to girls, the ratio is 14 to 15.
- Probability is the chance of something happening. Probability describes whether an event is likely to happen, unlikely to happen, certain to happen, impossible, or more likely, equally likely, or less likely to happen than another event.
- A result of an experiment is called an outcome or event. Possible outcomes are all the possible results or events that might happen.
- Probability of drawing a card: There are 52 cards in a deck so what are the chances of picking a King?
There are 4 Kings in a deck of cards so the probability of drawing a King would be 4 out of 52.
- Probability of flipping a coin and getting Heads or Tails: There are 2 sides to a coin so what is the chance of getting a heads or tails if you flip the a coin?
There is a 1 in 2 chance of getting a head or tail. Remember every time you flip the coin it is always a 1 in 2 chance of getting a head or tail no matter how many times you flip.
- Probability of rolling dice: If you roll 1 di what is the chance of rolling a 2?
There are 6 sides to a di so and only 1 side of the di has a two. The chance of rolling a 2 is 1 in 6.
- What if you have 2 dice? What would be the chance of rolling the dice and having the dice equal 5? Remember you can get five with 4 + 1 and 2 + 3.
Making a chart like the one above is very helpful in this type of problem. There are 36 possible outcomes. 4 of the outcomes will equal 5 so you have a 4 in 36 chance.
- Probability of picking an item: See the examples below --
- Probability of landing on a color on a spinner: What is the probability of landing on yellow when you spin the spinner?
There is 1 yellow space on the spinner. There are 4 equal spaces on the spinner. The chance on landing on yellow is 1 in 4.
- You can also use probability to determine if a game is fair or unfair. The teacher gives 1 student spinner A and she gives another student spinner B. She then explains that to win a game the person who spins yellow the most will win. Is this game fair or unfair?
A 
B
B
This game is unfair. The student with spinner A has less of a chance to spin yellow than the student with spinner B. Spinner A has a 1 in 4 chance. Spinner B has a 1 in 3 chance.
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