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Algebra 2B Section 11.2 Notes: Distributions of Data Constructing Histograms and box and whisker plots on the Graphing Calculator Mean: The sum of the data values divided by the number of data values. Median: The middle value, or the mean of the middle values of a data set, when the data are in numerical order. Standard Deviation: a measure of how spread out numbers are, it is the square root of the variance of the data. Symmetric Data: Use Mean and Standard Deviation 34% 34% 13.5% 13.5% 2.35% 0.15% 2.35% 0.15% Statisticians use measures of position to describe where specific values fall within a data set. Quartiles are three position measures that divide a data set arranged in ascending order into four groups, each containing about 25% of the data. The median marks the seconf quartile Q2 and seaparates the data into upper and lower halves. The first or lower quartile, Q1, is the median of the lower half, while the third or upper quartile, Q3, is the median of the upper half. The three quartiles, along with the minimum and maximum values, are called a five-number summary of a data set. Skewed Data: Use 5 Number Summary (the median, upper and lower quartiles, maximum and minimum) Calculator Instructions for Statistics Analysis (5-number summary) 1. Press STAT 2. Arrow over to CALC 3. Select 1-Var Stats and hit ENTER on the home screen x = Mean Sx = Sample Standard Deviation Q1 = 1st Quartile Q3 = 3rd Quartile Med = Median (2nd Quartile) Example 1: The number of hours Liana worked each week for the last 12 weeks were 21, 10, 18, 12, 15, 13, 20, 20, 19, 16, 18, and 14. a) Find the values for the 5-number summary. b) Interpret the summary. Example 2: The number of miles Brady ran each week for the last 10 weeks are 14, 8, 19, 16, 11, 9, 7, 16, 15, 12. a) Find the values for the 5-number summary. b) Interpret the summary. Calculator Instructions for Histogram (bar graph) and Box and Whisker Plots 1. Press STAT 2. Press EDIT 3. Enter the Data in the column L1, pressing enter after each selection. * To delete data: Highlight L1, Press CLEAR, Press ENTER 4. Turn on the Stat Plot Press 2ND y = Select Plot 1 Highlight ON, and Press Enter Select the type of graph you want to use (histogram is the 3 rd one over, box and whisker is 5th) Enter to select graph 5. Graph Press ZOOM 9 to fit the data in your window. Example 3: Ms. Shroyerâ€™s students each gave a presentation as part of their class project. The length of each presentation is shown in the table. Use a graphing calculator to create a histogram. Example 4: Eddie looked up prices for floor speakers for his basement. The prices are shown in the table. Use a graphing calculator to create a histogram. Example 5: Eddie looked up prices for floor speakers for his basement. The prices are shown in the table below. Describe the center and spread of the data using either the mean and standard deviation or the five-number summary. Justify your choice. Steps: 1. Make a box and whisker plot to describe the shape of the distribution (skewed or symmetric) o o If the data is skewed, use the five-number summary to describe the center and spread of the data. If the data is symmetric, use the mean and standard deviation to describe the center and spread. Example 6: The hourly wages for a random sample of employees of a restaurant are shown in the table. a) Use a graphing calculator to create a box-and-whisker plot. Then describe the shape of the distribution. b) Describe the center and spread of the data using either the mean and standard deviation or the five-number summary. Justify your choice. Example 7: The number of years of playing experience for each player on an over 30 recreational soccer team are shown in the table. Describe the center and spread of the data using either the mean and standard deviation or the five-number summary. Justify your choice Example 8: Tyler and Jordan are working through several brainteasers on the computer. The time in minutes that it took to complete each game is shown. Use a graphing calculator to create a box-and-whisker plot for each data set. Then describe the shape of each distribution. Example 9: The daily high temperatures over a 20-day period for two cities are shown. Use a graphing calculator to create a box-andwhisker plot for each data set. Then describe the shape of each distribution. Example 10: The number of participants for two sports at a summer camp for the past 15 sessions is shown. Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice.