Statistics and Probability

Gary eats a huge breakfast everyday Gary eats a huge breakfast everyday. His breakfast usually has 3 items which may include pancakes, cereal, eggs, bacon, and sausage. How many different breakfast combinations can he have? What if he added one drink option of orange juice or milk?

Statistical Questions Has to be testable Has to be measurable Has to have no bias

In a survey of a random sample of 500 students, 3 out of 5 students said they visited a library weekly. How many of the 500 students did not visit a library weekly?

Statistics Definitions Population – all of the individuals that fit a given description Sample –a smaller group from a population used to gather data about that population Representative Sample – a sample that can be considered the same as the results from the entire population Convenience Sample –a sample that is easy and quick to survey Random Sample –a sample where every individual in the population has the same chance of being included Bias – the difference between what the responses of a sample are and what the actual responses from the entire population would be

The students in a swimming class. Identify if you would use a sample to learn about each group. Explain your reasoning: The students in a swimming class. No; students could be surveyed individually. The attendees at an NBA basketball game Yes; there are too many to interview individually. The employees of a large company. The members of a string quartet. No; the musicians could be surveyed individually.

Explain why each sample may not be representative. A written survey is mailed to 8 houses in a neighborhood. Not everyone may fill out the surveys and return them. 200 people are called at home between 2pm and 3 pm. Someone may not be home or not answer the phone. People with last names beginning with “S” are called to answer a survey. It does not include anyone with a last name beginning with the other 25 letters of the alphabet.

The first ten people to enter a room are given a survey. Identify whether each sample is a convenience sample or a random sample: The first ten people to enter a room are given a survey. Convenience Every tenth person entering a the mall is given a survey. Random All the names of the 3rd graders in the school are put in a hat and 15 names are drawn. The last 12 people standing in line to get tickets to a movie.

A veterinarian asks dog owners about a new brand of hamster food. Identify the source of bias. Then reword the question to remove the bias: A veterinarian asks dog owners about a new brand of hamster food. The vet should be asking people who own hamsters. A veterinarian asks hamster owners about a new brand of food. People at a rock concert are asked if Dolly Parton is a good singer. People at a punk rock concert probably don’t listen to country music. People at a rock concert are asked if Linkin Park is a good band.

The quotient of two whole numbers is 4 The quotient of two whole numbers is 4. The product of the numbers is 144. What are the two numbers? (24 and 6)

Measures of Central Tendency Mean – the average (add all #’s and divide by how many #’s there were originally) Median – the middle # in a data set when the data are arranged from least to greatest. Mode – the # of #’s that appear most often in the data set. (Sometimes there are none, sometimes there can be more than one.) Range – the difference between the greatest and the least values in a data set. Outlier – a # or #’s whose values are much less or much greater than the other #’s in a data set

3,6,7,6,2,6 12, 17, 11, 12, 13 4.6, 3.9, 2.1, 2.9, 3.1, 4.0, 3.9 1, 1, 2, 4, 1, 3, 5, 19, 6 20, 22, 24, 25, 25, 3, 21 Mean Median Mode Range Outliers

Lena bought 6 apples and 6 oranges and paid a total of $7. 80 Lena bought 6 apples and 6 oranges and paid a total of $7.80. The apples cost $0.50 each. What did each orange cost?

Clusters, Gaps, and Outliers Cluster – a group of data points that are close to each other. Gap – a region where there are no data plots. Line Plot – a diagram that organizes data using a number line.

Mean Median Mode Range Outliers Clusters Gaps 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 10 Mean Median Mode Range Outliers Clusters Gaps 0, 0, 1, 1, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 10, 10 0, 0, 1, 4, 4, 4, 4, 4, 5, 5, 6, 7, 10, 10, 10, 10

Rewrite without bias: What is your favorite flavor, chocolate or vanilla? Which team is better, the Broncos, or the 49ers? Do you want to go to Florida or Alaska? Who is the best singer, Madonna or Elvis? Are dogs or cats the best pets?

How many siblings are in your family? What is your favorite holiday? What is your favorite sport? How tall are you? What size shoes do you wear? How many cars does your family own? How many hours of TV do you watch a week? Who is your favorite Disney character? Where was the last place you ate out for dinner?

Tell me what kind of information you would show with each of the following: Line /Dot Plot Line Graph Bar Graph Histogram Pictogram Box and Whisker Pie Chart Stem and Leaf Tally Mark T-chart

Tally Mark T-chart Used to Show: Example:

Line/Dot Plot Used to show: Example:

Stem and Leaf Used to Show: Example:

Pictogram Used to Show: Example:

Line Graph Used to show: Example:

Bar Graph Used to show: Example:

Histogram Used to show: Example:

Pie Chart Used to Show: Example:

Histogram Used to show data in intervals rather than individual data points. Interval = set range that is repeated to split data into smaller portions

Box and Whisker Used to Show: extremes, median, lower and upper quartiles. Lower Extreme: the least value in a box-and-whisker plot. Upper Extreme: the greatest value in a box-and-whisker plot. Lower Quartile: the median of the lower half of a data set in a box-and-whisker plot. Upper Quartile: the median of the upper half of the data set in a box-and-whisker plot.

Lower Extreme: Upper Extreme: Median: Lower Quartile: Upper Quartile: 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 10 Lower Extreme: Upper Extreme: Median: Lower Quartile: Upper Quartile: Outliers 0, 0, 1, 1, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 10, 10 0, 0, 1, 4, 4, 4, 4, 4, 5, 5, 6, 7, 10, 10, 10, 10