Statistics and Probability

Statistics and Probability I can define and calculate the three measures of center. I can determine which measure of center best represents the data. I can determine if a sample represents a population. I can explain how random sampling produces a more accurate representation. I can use random samples to draw conclusions about a population.

I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center What are they? Why do we use them? Why do we need all three?

I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center Find the mean, median, and mode of each data set. 46, 35, 23, 37, 29, 53, 43 Mean: Median: Mode:

I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center Find the mean, median, and mode of each data set. 72, 56, 47, 69, 75, 48, 56, 57 Mean: Median: Mode:

I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center The values in a data set are: 12, 11, 8, 6, 9, 8 Answer: 9 What was the question?

I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center The values in a data set are: 10, 7, 9, 5, 13, 10 Answer: 9.5 What was the question?

I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center Josh’s test scores follow: 95, 89, 87, 95, 86, and 88 If Josh could have his choice of the three measures of center to be his final grade, which measure of center should he choose?

I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center Begin Homework: Measures of Center Practice Wkst

I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Think-Pair-Share: Which measure of center would you use to BEST represent the data? Test Scores 88, 94, 90, 85, 88, 94, 79, 94, 88, 24

I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Think-Pair-Share: Which measure of center would you use to BEST represent the data? Concession Stand Soft Drink Purchases 2.00, 1.00, 2.00, 1.50, 2.00, 1.50, 2.00, 2.00, 1.00, 1.50, 2.00, 2.00, 2.00, 1.00, 2.00 (Lg: $2.00; Med: $1.50; Sm: $1.00)

I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Think-Pair-Share: Which measure of center would you use to BEST represent the data? Middle School Student Ages 10, 11, 12, 12, 14, 11, 12, 10, 11, 14, 13, 13, 14, 14, 12, 10, 12, 11, 12, 11, 13, 14, 14, 13, 10

I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center: Which best represents the data? Meanis preferred… • most often • when an average is desired Median is preferred… • when you know that a distribution is skewed • when there is an outlier • when you have a small number of subjects Modeis preferred… • rarely • when describing discrete categorical data

I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Think-Pair-Share: Which measure of center would you use to BEST represent the data? Ages of Lions at Zoo 18, 4, 3, 7, 1, 6, 5, 4

Measures of Variation - Vocabulary Review Range - The difference between the greatest data value and the least data value Quartiles - are the values that divide the data in four equal parts. Lower (1st) Quartile(Q1) - The median of the lower half of the data. Upper (3rd) Quartile(Q3) - The median of the upper half of the data. Interquartile Range - The difference of the upper quartile and the lower quartile. (Q3 - Q1) Mean absolute deviation - the average distance between each data value and the mean.

Box-and-Whisker Plots

Vocabulary • Box and Whisker Plots – a plot that uses a number line to show the distribution of a set of data • Lower Quartile – the median of the lower half of data • Upper Quartile – the median of the upper half of data • Interquartile Range – the difference between the lower and upper quartiles

Why use a Box-and-Whisker?? • To analyze how data in a set are distributed • To compare two sets of data

Box-and-Whisker Smallest value Largest value

How to Make a Box-and Whisker Plot • Arrange the data from least to greatest. • Make a number line for that data. • Find the median of the entire set of data. MIDDLE LINE IN BOX • Find the lower quartile (the median of the lower half). LEFT SIDE OF BOX • Find the upper quartile (median of the upper half). RIGHT SIDE OF BOX • Find the smallest and largest values. WHISKERS

Example #1 How do we represent this data in a box and whisker plot? 19, 21, 17, 20, 17, 28, 26, 23, 29

Example #2 How do we represent this data in a box and whisker plot? 44, 56, 47, 48, 55, 55, 58, 50, 52

Interquartile Range – the difference between the lower and upper quartiles The IQR allows one to measure variability of the middle 50% of the data.

Test 1 Grades: 60, 65, 65, 65, 65, 70, 70, 70, 75, 75, 75, 80, 85, 85, 90 45 50 55 60 65 70 75 80 85 90 100 What is the interquartile range?

Test 2 Grades: 60, 75, 75, 80, 80, 80, 85, 85, 85, 85, 85, 90, 90, 90, 95 45 50 55 60 65 70 75 80 85 90 100 What is the interquartile range?

I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Your task is to find the average height of students at WMS. How could you do this? What problems might you face? A sample is used to make a prediction about an event or gain information about a population. A whole group is called a POPULATION. A part of a group is called a SAMPLE.

I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. A whole group is called a POPULATION. A part of a group is called a SAMPLE. When biologists study a group of wolves, they are choosing a sample. The population is all the wolves on the mountain. Population Sample

I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. A random sample is a sample in which each individual or object in the population has an equal chance of being selected. Random sample? To find out how Wilmington residents feel about coffee, a survey is given to customers at a coffee shop. Random sample? To find the average number of video games owned by students at WMS, every 5th student to arrive at school in the morning is given a survey.

I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. A sample is biased if individuals or groups from the population are not fairly represented in the sample. - A random sample is unbiased. • Example of Bias: • To find out about your classmates’ favorite sports, you ask only a table full of football players • To find out how people feel about the importance of college, you ask only your teachers • To find out Americans’ favorite college football team, you ask only Ohio natives

I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. A sample is representative of the population when individuals or groups from the population are fairly represented in the sample (unbiased). Is the sample representative of the population? To determine America’s favorite athlete, Sports Illustrated subscribers are asked to complete a survey. Is the sample representative of the population? To determine Americans’ approval/disapproval of its politicians, students across the country are given a survey during lunchtime.

I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. A sample can help us draw conclusions about a population. Example: Tom is running for class president. After random sampling 50 of his classmates, 32 of them said they will vote for him. If there are 325 students at his school, about how many votes can he expect to receive?

I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. A sample can help us draw conclusions about a population. Example: Mary is inspecting a building’s lighting. 5 out of 12 light bulbs checked need replaced. If the entire building has 140 light bulbs, about how many bulbs will need replaced?

I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Sampling Practice Wkst

I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Sampling Review 1.) Kellogg’s receives a complaint about one of their cereals. Their taste testing team decides to sample their recent production by testing the first 100 boxes off the production line. Did the team’s sampling method accurately represent the population? Explain. 2.) To improve their sampling method, Kellogg’s decides to test the first 200 boxes off the production line. Is this sample better representing the population? Explain.

I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. The guidance counselors want to organize a career day.  They will survey all students whose ID numbers end in a 7  about their grades and career counseling needs. Would this  situation produce a random sample? Explain your answer. A Yes B No

I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. The local newspaper wants to run an article about reading habits in your town. They conduct a survey by asking people in the town library about the number of magazines to which they subscribe. Would this produce a random  sample? Explain your answer. A Yes B No

I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. The chart shows the number of people wearing different types of shoes in Mr. Thomas' English class. Suppose that there are 300 students in the cafeteria. Predict how many would be wearing high-top sneakers. Shoes Number of Students

Data Review Carla took a random sample of 7th graders at her school to see what type of vehicle is preferred most in her grade. • What was Carla’s sample size? • If there are 235 students, estimate the actual number of students that like trucks most.

Data Review Create a box and whisker plot. What is the interquartile range? 20 25 30 15 10

Statistics and Probability I can classify the probability as impossible, unlikely, equally likely, likely and certain. I can represent probability with fractions and percents. I can use data to predict the probability of an event occurring. I can use theoretical and experiential probability to solve problems.

Probability One way to express probability is to use a fraction. Number of favorable outcomes Total number of possible outcomes Probability of an event =

Probability Example: What is the probability of flipping a nickel and the nickel landing on heads? Step 1: What are the possible outcomes? Step 2: What is the number of favorable outcomes? Step 3: Put it all together to answer the question. The probability of flipping a nickel and landing on heads is: 1 . 2

Probability can be expressed in many forms. For example, the probability of flipping a head can be expressed as: 1 or 50% or 1:2 or .5 2 The probability of randomly selecting a blue marble can be expressed as: 1 or 1:6 or 16.7% or .167 6

When there is no chance of an event occurring, the probability of the event is zero (0). When it is certain that an event will occur, the probability of the event is one (1). Equally Likely Impossible Certain Likely Unlikely 0 1 2 1 4 3 4 1 The less likely it is for an event to occur, the probability is closer to 0 (i.e. smaller fraction). The more likely it is for an event to occur, the probability is closer to 1 (i.e. larger fraction).

Without counting, can you determine if the probability of picking a red marble is lesser or greater than 1/2? It is very likely you will pick a red marble, so the probability is greater than 1/2 (or 50% or 0.5) What is the probability of picking a red marble? Click 5 6 Click Add the probabilities of both events. What is the sum? 1 + 5 = 1 6 6 Click

Note: The sum of all possible outcomes is always equal to 1. There are three choices of jelly beans - grape, cherry and orange. If the probability of getting a grape is 3/10 and the probability of getting cherry is 1/5, what is the probability of getting orange? 3 + 1 + ? = 1 10 5 ? The probability of getting an orange jelly bean is 5 . 5 + ? = 1 10 ?

Arthur wrote each letter of his name on a separate card and put the cards in a bag. What is the probability of drawing an A from the bag? A 0 B 1/6 C 1/2 D 1 A U R T H R

Statistics and Probability