Unit 2: Lesson 10 Measures of Spread Name:

Transcription

1 Unit 2: Lesson 10 Measures of Spread Name: Part 1: Mean Absolute Deviation (nice, but not the measure of spread we ll use ) The heights, in inches, of the players on a basketball team are given below a) Use the number line below to create a dot plot of the player heights. b) Compute the mean (average) of the player s heights. Mark this value in the dot plot above. Mean height = c) Compute the mean absolute deviation of the player heights. The table below has been provided as an aid in computing this value. Data Value 84 Mean Absolute Deviation Mean absolute deviation = Unit 2 Quantitative Variables 1

2 2. Weight of Football Players The weights, in pounds, of the seven players from a high school football team are given below a) Use the number line below to create a dot plot of the player weights. b) Compute the mean (average) of the player s weights. Mark this value in the dot plot above. Mean weight = c) Compute the mean absolute deviation of the player weights. The table below has been provided as an aid in computing this value. Data Value 165 Mean Absolute Deviation Mean absolute deviation = Unit 2 Quantitative Variables 2

3 Part 2: Standard Deviation (another reason the Ti-84 is so beautiful ) Problem #3: The following data is a list of average life spans (in years) of several different animals a) Calculate the mean. = averagelife_span b) Complete the table below. (years) (years) (years) 2 (years 2 ) c) Find the total sum of the errors. d) Find the total sum of the squares of errors. = 2 = e) Divide the sum from part d by (n-1). This is called the variance of the data. 2 s 2 n 1 = f) Finally, take the square root of your answer to part e. This is called the standard deviation of the data. It is a measure of spread. s 2 n 1 = Unit 2 Quantitative Variables 3

4 Problem #4: Total Points for NFL Teams The following numbers are the total points for 8 randomly selected NFL teams a) What is the mean of this data? b) Complete the table below. (pts) (pts) (pts) 2 (pts 2 ) c) Find the total sum of the errors. d) Find the total sum of the squares of errors. = 2 = e) Divide the sum from part d by (n-1). This is called the variance of the data. f) Finally, take the square root of your answer to part e. This is called the standard deviation of the data. It is a measure of spread. 2 s 2 n 1 = s 2 n 1 = g) Use your TI-84 to compute the standard deviation. What did you get? Unit 2 Quantitative Variables 4

5 Problem #5: 4 th Grade Basketball The following numbers are the heights in inches of players on a 4 th grade basketball team. 53, 48, 57, 48, 51, 52, 59 a) Use the line below to draw a dot plot. Draw a vertical line to represent where the mean weight of the players is. b) Complete the table below. (in) (in) (in) 2 (in 2 ) c) Find the total sum of the errors. d) Find the total sum of the squares of errors. = e) Divide the sum from part d by (n-1). This is called the variance of the data. 2 = f) Finally, take the square root of your answer to part e. This is called the standard deviation of the data. It is a measure of spread. 2 s 2 n 1 = s 2 n 1 = g) Go back to the graph and draw vertical lines that are 1 standard deviation above the mean and 1 standard deviation below the mean. How many players are within 1 standard deviation of the mean? Unit 2 Quantitative Variables 5

6 6. Let s summarize the statistics for our 4 th grade basketball team. We know two of these statistics already. Median height = IQR = Mean Height = Stand. Dev. = 7. Now, suppose that Aaron Gray (who used to play for the Chicago Bulls) decides to join the 4 th grade team. Aaron is 7 feet tall. (84 ). a) Enter the heights of the original team and Aaron Gray into your calculator. b) Calculate the 1-variable stat s and record the new team s statistics below. Median height = IQR = Mean Height = Stand. Dev. = c) Which of the statistics were most affected by Aaron Gray joining the team? What s the Moral of this statistics story? Unit 2 Quantitative Variables 6