Math Across the Curriculum: Statistics and Probability Paraprofessional Training August 24 th – August 28th

Pictographs Definition of Pictograph Pictograph is a way of representing statistical data using symbolic figures to match the frequencies of different kinds of data.

Bar Graph Definition of Bar Graph A bar graph is a graph that compares different amounts using bars.

Histogram Definition of Histogram A histogram is a bar graph that shows how frequently data occur within certain ranges or intervals. The height of each bar gives the frequency in the respective interval.

Stacked Bar Graph Definition of Stacked Bar Graph Stacked bar graph is a graph that is used to compare the parts to the whole. The bars in a stacked bar graph are divided into categories. Each bar represents a total.

Line graphs Line graph is a graph that uses line segments to connect data points and shows changes in data over time. More about Line Graph Multiple Line Graph: Multiple line graph is a line graph that shows changes in data over time for more than one category.

Stem and Leaf Plot Definition of Stem-and-Leaf Plot Stem-and-Leaf plot is a method of organizing numerical data in order of place value. The 'ones digit' and the 'tens digit and greater' of each data item is seperated as leaves and stems respectively.

Stem and Leaf Plot The stem-and-leaf plot below shows the number of students enrolled in a dance class in the past 12 years. The number of students are 81, 84, 85, 86, 93, 94, 97, 100, 102, 103, 110, and 111.

Circle graphs Definition of Circle Graph A circle graph is a graph in the form of a circle that is divided into sectors, with each sector representing a part of a set of data.

Line plot Definition of Line Plot A line plot shows data on a number line with x or other marks to show frequency.

Scatter Plot Definition of Scatter Plot A scatter plot is a graph made by plotting ordered pairs in a coordinate plane to show the correlation between two sets of data.

Frequency Table Definition of Frequency Table A frequency table is a table that lists items and uses tally marks to record and show the number of times they occur.

Function Table A function is a relationship between two quantities in which one quantity depends on the other. A function is a many- to-one (or sometimes one-to-one) relation.

Graphing relationships The data from an input / output table can be graphed on a coordinate grid Input (x) Output (y)

Slope of the line Definition of Slope Slope is the measure of steepness of a line.

Mean (average) Data: 1, 5, 4, 3, 7

Mean (average) Normally we teach the formula for finding the average (mean) Add the values of all the data given and then divided the sum by the number (quantity) of data = ÷ 5 = 4

Average (mean) The mean (average) can also be found be evenly distributing the values

Find the mean A random sample of 7 teachers were asked how many hours worth of sleep they got the night before the first day of school Their responses were:  6, 8, 3, 6, 4, 6, 2

Mean, mode, median & range The mean (average) amount of sleep those teachers got was 5 hours Use the same data from the teacher’s survey to find the mode (most common)  6, 8, 3, 6, 4, 6, 2 Now rearrange the data to find the median (middle value): 2, 3, 4, 6, 6, 6, 8 The data ranges from 2 to 8 or has a range (distance between high and low values) of 6

Mean, Median & Mode Find the values of the 5 items of data that have a range of 9, a mean of 11, a median of 12, and a mode of 15. _____, _____, _____, _____, _____

Driving decisions The Downing family is planning a 6-day vacation in Denver. Danny searches the web for car rental rates and find the following deals:  Car A: $199 per week, unlimited mileage  Car B: $172 per week, up to 300 miles with a rate of 15¢ per mile after the first 300  Car C: $25 per day, 10¢ per mile

Driving decisions Danny expects to put some where between 400 and 500 miles on the rental car Which rental plan would give Danny the best deal?  Car A: $199 per week, unlimited mileage  Car B: $172 per week, up to 300 miles with a rate of 15¢ per mile after the first 300  Car C: $25 per day, 10¢ per mile Take a break while you work on this problem.

Driving decisions Which rental plan do you recommend for Danny? How did you decide on the best deal for Danny’s family? At what point does one plan become better than another plan? Did anyone graph it?

Organizing information visually

The Arm-Wrestling Contest 6 Boys: Brady, Connor, Malik, Jeremy, Mark, and Dave are having an Arm-Wrestling Contest Each boy will wrestle the others once to see who will be the champion. How many arm-wrestling matches will they need to have in order to find the winner?

Creating a Sample Space Brady Connor Malik Jeremy Mark Dave

What are the chances for Mark? Mark is very hesitant about going first. He doesn’t want to admit that he has never arm-wrestled before. He is thinking he has a one in 6 chance of going first? What is the probability that Mark will be chosen to arm-wrestle in the 1 st match?

What are the chances for Mark? What is the probability that Mark will not be involved in the first match?

Probability The probability of the occurrence of an event can be expressed as a fraction, a percent or as a decimal between 0 and 1 0% - never happening, no chance 50% - could go either way 100% - no doubt, it will happen

What are the odds? What is the probability that I will win the drawing if the odds are 2 to 1 against me winning the drawing? Odds can be expressed “for” or “against” and will compare the two outcomes over time 2 to 1 odds against me winning is predicting two losses for each win With these odds, I only have a 1 out of 3 chance (about 33%) of winning.

Let’s Make a Deal! 123

Should I stay or switch doors? Is the contestant better off staying with her / his original choice? Why? Turn and talk to others at your table…

Let’s Play! One Game Show Host per table One player One recorder Play 24 rounds. Record decisions to stay or switch Record wins and losses

To stay or to switch doors? Goat Car YesX Switch! XYes Switch! XYes Stay!

Who is right? My mother chooses the same numbers every time she plays Take 5 because she is under the assumption that her numbers are bound to roll in one day. My father always allows the computer to randomly choose his numbers for him because he thinks my mother is ridiculous and overly superstitious. Who do you agree with and why? Turn and talk to a neighbor.