70B. Box and Whisker Plots. Vocabulary: Mean. Median. Mode. Range. Upper Extreme. Upper Quartile. Lower Extreme. Lower Quartile. Inter-Quartile Range

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1 Algebra 1: Statistics Vocabulary: Mean Name: Block: 70B Median Mode Range Upper Extreme Upper Quartile Lower Extreme Lower Quartile Inter-Quartile Range Box and Whisker Plots

2 Calculator Steps for Mean, Median, Mode, Range, Quartiles, Box and Whiskers To clear a list: STAT 1. EDIT L1 CLEAR To input your data: STAT 1. EDIT L1 Input all of your data in L1 To calculate: STAT CALC 1. 1-var Stats ENTER ENTER Example: Find the indicated values and create a box and whiskers plot for the given data. 10, 12, 12, 15, 16, 17, 18, 20, 24 Mean = Median = Mode = Range = Upper Extreme = Upper Q = Lower Extreme = Lower Q = 1) For the box-and-whisker plot above, find the following values: Upper Extreme: Lower Extreme: Upper Quartile: Median: Lower Quartile: What is the interquartile range?

3 2) 3) A weather website lists the amount of rainfall in Springfield and Fort Sidbottom over the month of February. These box-and-whisker plots show the results. What city has a lower quartile that is higher than the other? What city has a higher quartile that is higher than the other? 4) A video camera was set up on a highway to record the speeds of passing cars. This box-and-whisker plot shows the results. What percentage of cars traveled between 60 and 70 mph? What is the range of the freeway speeds? Upper Extreme: Lower Extreme: Upper Quartile: Median: Lower Quartile:

4 5) a) What is the interquartile range b) of: In which quartile would a score of 40 fit? What is the range of: c) d) What is the lower quartile, upper quartile and median of: ) 7) 8)

5 9) a) I and II only b) I and III only c) II and III only d) II only 10)

6 11) 12) Identify the true statement.

7 13) 14) Bloomfield Emerald From the list below, choose the best description for each city and write it in the blank provided.

8 SCATTERPLOTS & LINE/CURVE OF BEST FIT: Data correlation: When the data points form a straight line on the graph, the linear relationship between the variables is stronger and the correlation is higher (Figure 1). This is called correlation. This is called correlation. This is called correlation. If you cannot draw a line, then we say there is correlation! Line of Best Fit: The line that most accurately models the plotted data points. To input your X and Y values: STAT 1. EDIT L1 L1 x values L2 L2- y values STAT CALC LinReg Med-Med (ax+b) ENTER **Line of Best Fit is often called the prediction equation or the Linear Regression.

9 DIRECTIONS: Use your TI-84 calculator to calculate the line for each set of data: Ex1 x Height (in) y Weight (lbs) a) Equation for the best fitting line: b) Predict how much a 6 foot 5 inch person would weigh: Ex2 x Experience (weeks) y Typing Speed (wpm) a) Equation for the best fitting line: b) Predict the typing speed of a student with 11 weeks of experience: c) Predict the weeks of experience for a student who can type 35 wpm: 15) The Cody Company ran a study on its sales force and learned that the average number of years of experience for each sales team was in direct relation to annual sales volume. x Average Yrs of Experience y Annual Sales (in thousands) Equation for the best fitting line: 16) The table below shows the sales for eight encyclopedia sales representatives during a given period and the years of experience of each representative. x Yrs of Experience y Amount of Sales $9000 $6000 $4000 $3000 $3000 $5000 $8000 $2000 Equation for the best fitting line:

10 Scatterplots and Line of Best Fit 17) 18) 19)

11 20) 21) 22) The following data pairs (x, y) give the population y (in millions) of Virginia x years after Write the best-fitting line for the data. (Please note that data is not accurate). Assuming the population continues in a linear path, what would the population be in the year 2015? (0, 9.7), (1, 10.2), (2, 10.6), (3, 10.9), (4, 11.3), (5, 11.7), (6, 12.1), (7, 22.5) 23) The data pairs (x, y) give U.S. average annual public college tuition y (in dollars) x years after Write the best-fitting line for the data. (Again, data is not accurate). Assuming tuition continues its linear path, what would the tuition be in 2017? (0, 5271), (1, 5360), (2, 5430), (3, 3506), (4, 3562), (5, 5727), (6, 5928)

12 24) For water to vaporize, it must break its bonds and overcome air pressure. It is air pressure which helps keep water a liquid. Therefore as you go up in elevation, the air is thinner and the boiling point of water becomes lower and lower. The following data (x, y) show boiling points (y) at different elevations (x). Write a best-fit line for the data where x represents elevation and y represents boiling point. Use this best-fit line to determine what the boiling point would be at 14,000 feet. (2000, 208.4), (4000, 204.8), (6000, 201.1), (8000, 197.4), (10000, 193.6), (12000, 189.8) (**Yes, above science and data are quite accurate**) Curve of Best Fit: The quadratic function that most accurately models the plotted data points. To input your X and Y values: STAT 1. EDIT L1 L1 x values L2 L2- y values STAT CALC 5. Quad-Reg ENTER 25) A pumpkin tossing contest is held each year in Illinois where people compete to see whose catapult will send pumpkins the farthest. A certain catapult will launch pumpkins from 25 feet above the ground at a speed of 125 feet per second. The chart below shows the horizontal distances (in feet the pumpkins travel when launched at different angles. Use your graphing calculator to find the best-fitting quadratic model for the data. **Remember x is the independent variable and y is dependent? Does distance depend on angle? Angle (degrees) Distance (feet) a. What is your best-fitting quadratic model? Y = b. At what angle would the pumpkin travel the farthest? Explain how you find your answer. Angle = º

13 26) Determine the quadratic curve of best fit for the following data: {(-3, 2), (0,5), (1, 7.3), (-1, 3.3), (-6, 5), (-7, 7.3)} a. What is the equation for curve of best fit? Y = b. Estimate the value of y when x = ) Determine the quadratic curve of best fit for the following data: { (-8, 80.4), (-7, 57.8), (-6, 38.6), (-5, 22.8), (3, 18.8), (5, 51.8), (7, 98.4)} a. What is the equation for curve of best fit? Y = b. Estimate the value of y when x = )

14 29) The set of ordered pairs shows a relationship between x and y. ( 3,20),( 1, 3),(0, 6),(2,6),(4,40),(6,102) Which equation best represents this relationship? a) y 9.31x b) y 11.5x 6 c) d) y x x y x x ) Using the equation chosen in #29, what is the value of y, rounded to the nearest whole number, when the value of x is 8? 31) The set of ordered pairs shows a relationship between x and y. (0, 2),(3,7),(6,16),(6,15),(8,21),(10,28),(11,31) Using the line of best fit, which is the closest to the output when the input is 5? a) 2.7 b) 11.5 c) 12.7 d) ) Which equation best models the relationship shown on the grid? a) y 2x 8 b) y 2x 8 c) d) y x x y x x