SCATTER PLOTS AND LINES OF BEST FIT

An effective way to see a relationship in data is to display the information as a __________________. It shows how two variables relate to each other by showing how closely the data points _______ to a line. scatter plot fit The following table presents information on tornado occurrences. Make a scatter plot for the table. Year 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 # of Tornadoes 201 593 616 897 654 919 866 684 1133 1234

Do you notice a trend? Year 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 # of Tornadoes 201 593 616 897 654 919 866 684 1133 1234 1200 1000 800 600 400 Do you notice a trend? 200 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995

Scatter plots provide a convenient way to determine whether a ___________ exists between two variables. correlation positive A __________ correlation occurs when both variables increase. negative A ___________ correlation occurs when one variable increases and the other variable decreases. If the data points are randomly scattered there is _______ or no correlation. little

little or no correlation Positive correlation Negative correlation little or no correlation

Example 1: The scatter plots of data relate characteristics of children from 0 to 18 years old. Match each scatter plot with the appropriate variables studied. 1. age and height 2. age and eye color 3. age and time needed to run a certain distance no correlation between age and eye color as your age increases your height also increases 2 1 as your age increases the time will decrease 3

Sometimes points on a scatter plot are represented by a trend line or a _______________________. You can study the line to see how the data behaves. You may have a basis predict what the data might be for values not given. line of best fit Example 2: Find the line of best fit for the scatter plot you made on the first page. To fit the line to the points, choose your line so that it best matches the overall trend. The line does not have to pass through any of the points.

Use the line of best fit to predict how many tornadoes may be reported in the United States in 2015 if the trend continues. 1200 1000 800 600 If the trend continues we predict that there will be 1200 tornadoes reported in 2015. 400 200 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

If the data points are close to the line of best fit, it is said to have a ___________correlation. strong strong positive weak positive strong negative weak negative

Box and Whisker Plot 5 Number Summary for Odd Numbered Data Sets

Finding the Median of Odd Numbered Data Sets Once the pieces of data (numbers) are arranged in order from least to greatest, then the middle number of the set is the median [3, 4, 4, 5, 8, 8, 9, 10,11] The median for this set of data = 8

Odd Numbered Data Sets The median splits the data set in half. [3, 4, 4, 5,] 8, [8, 9, 10,11] From here we can then find the upper and lower quartiles as well as the upper and lower extremes.

The lower quartile for this set of data = 4 The lower quartile is the median of the bottom half of the data (to the left of the median). If the part of the set we are considering has an even number pieces of data, you must find the mean of the two middle pieces of data to get the lower quartile. [3, 4, 4, 5,] 8, [8, 9, 10,11] 4 + 4 = 8 8 divided by 2 = 4 The lower quartile for this set of data = 4

Upper Quartile The upper quartile is the median of the top half of the data (to the right of the median). If the part of the set we are considering has an even number pieces of data, you must find the mean of the two middle pieces of data to get the upper quartile. [3, 4, 4, 5,] 8, [8, 9, 10,11] 9 + 10 = 19; 19 divided by 2 = 9.5 The upper quartile for this data set = 9.5

Interquartile Range To find the interquartile range, subtract the lower quartile from the upper quartile. [3, 4,] 4 [4, 5,] 8, [8, 9] 9.5 [10,11] Upper Quartile – Lower Quartile = _____ 9.5 – 4 = 5.5 The interquartile range for this data = 5.5

Lower Extreme The lower extreme is the lowest number in the data set. [3, 4,] 4 [4, 5,] 8, [8, 9] 9.5 [10,11] The lower extreme for this data set = 3

Upper Extreme The upper extreme is the highest number in the data set. [3, 4,] 4 [4, 5,] 8, [8, 9] 9.5 [10,11] The upper extreme for this data set = 11

Range The range of the data can be found by subtracting the lower extreme from the upper extreme. [3, 4,] 4 [4, 5,] 8, [8, 9] 9.5 [10,11] 11 – 3 = 8 The range for this data set = 8

5 Number Summary Median = 8 Lower Quartile = 4 Upper Quartile = 9.5 [3, 4, 4, 5, 8, 8, 9, 10,11] Median = 8 Lower Quartile = 4 Upper Quartile = 9.5 Lower Extreme = 3 Upper Extreme = 11

Any Questions?

Sample Problem (ODD) Data Set [10, 10, 14, 15, 17, 20, 20, 21, 22]

Sample Problem (ODD) The 5 Number Summary for the sample problem with an even number of pieces of data is: [10, 10, 14, 15, 17,20, 20, 21, 22] Median= 17 Lower Quartile = 12 Upper Quartile = 20.5 Lower Extreme = 10 Upper Extreme = 22

Even Numbered Data Sets [ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20] Median = 7.5 Lower Quartile = 5 Upper Quartile = 11 Upper Extreme = 20 Lower Extreme = 2

Any Questions?

Sample Problem Use the following data set to create a 5 number summary 1,2,3,4,5,6,7,8,9,10,11,12

Sample Problem What is the 5 number summary? Median = 6.5 Lower Quartile = 3.5 Upper Quartile = 8.5 Upper Extreme = 12 Lower Extreme = 1

Any Questions?