Georgian College

• BDAT MISC

• Table of Contents TI-83 Plus and TI-84 Plus Graphing Calculators ............................................................................................ 4 Clear Lists.................................................................................................................................................. 4 Enter Data Into Lists.................................................................................................................................. 4 Create a Histogram for Ungrouped Data .................................................................................................. 5 Create a Histogram for Grouped Data ...................................................................................................... 6 Create a Frequency Polygon ..................................................................................................................... 7 Calculate Factorials, Permutations, and Combinations............................................................................ 7 Calculate a Binomial Probability Distribution ........................................................................................... 8 Calculate a Hypergeometric Probability Distribution ............................................................................... 8 Use the Binomial Cumulative Function..................................................................................................... 9 Use the Normal Cumulative Function....................................................................................................... 9 Calculate One-Variable Statistics for a Sample....................................................................................... 10 Create a Scatter Plot and a Line of Best Fit............................................................................................. 10 Generate Random Numbers................................................................................................................... 12 Create a Box and Whisker Plot................................................................................................................ 13 Microsoft Excel™......................................................................................................................................... 14 Enter Data into Cells................................................................................................................................ 14 Create a Histogram for Ungrouped Data ................................................................................................ 15 Create a Histogram for Grouped Data .................................................................................................... 17 Create a Frequency Polygon ................................................................................................................... 17 Calculate Factorials, Permutations, and Combinations.......................................................................... 18 Calculate a Binomial Probability Distribution ......................................................................................... 18 Calculate a Hypergeometric Probability Distribution ............................................................................. 18 Use the Binomial Cumulative Function................................................................................................... 19 Use the Normal Cumulative Function..................................................................................................... 19 Calculate One-Variable Statistics for a Sample....................................................................................... 19 Create a Scatter Plot and a Line of Best Fit............................................................................................. 20 Generate Random Numbers................................................................................................................... 21 Create a Box and Whisker Plot................................................................................................................ 22 Fathom™ ..................................................................................................................................................... 23 Enter Data into Attributes....................................................................................................................... 23 Create a Histogram for Ungrouped Data ................................................................................................ 24 Create a Histogram for Grouped Data .................................................................................................... 25 Create a Frequency Polygon ................................................................................................................... 26 Calculate Factorials, Permutations, and Combinations.......................................................................... 26 Calculate a Binomial Probability Distribution ......................................................................................... 27 Calculate a Hypergeometric Probability Distribution ............................................................................. 27 Data Management 12 Technology Appendix Page 3 Use the Binomial Cumulative Function................................................................................................... 28 Use the Normal Cumulative Function..................................................................................................... 28 Calculate One-Variable Statistics for a Sample....................................................................................... 29 Create a Scatter Plot and a Line of Best Fit............................................................................................. 29 Generate Random Numbers................................................................................................................... 30 Create a Box and Whisker Plot................................................................................................................ 32 Data Management 12 Technology Appendix Page 4 TI-83 Plus and TI-84 Plus Graphing Calculators The keys on the TI-83 Plus and TI-84 Plus are colour-coded to help you find the various functions. The colours described in this section apply to the TI-84 Plus. • The number keys, the decimal point key, and the negative sign key are white. When entering negative values, use the white negative (–) key, not the grey subtraction – key. • The grey keys on the right side are the math operations. • The grey keys across the top are used when graphing. • The secondary function of each key is printed in blue above the key and is activated by pressing the blue 2nd key. For example, to find the square root of a number, press 2nd then x2 to access [ ]. • The alpha function of each key is printed in green above the key and is activated by pressing the green ALPHA key. Clear Lists The TI-83 Plus and TI-84 Plus can store data in lists that can be further manipulated or analysed. To ensure that there is no extraneous data from a previous use of the lists, it is wise to clear the lists before entering data. • Press 2nd , then + to access the MEMORY menu, [MEM]. • Select 4:ClrAllLists, then press ENTER . Enter Data Into Lists • Press STAT . The cursor will highlight the EDIT menu. • Press 1 or ENTER to select 1:Edit... . The contents of the lists will display. You can enter new data, or edit existing data. There are six lists. Scroll to the right to see all of the lists. • To clear the data in a single list, press STAT , then select 4:ClrList. Press 2nd , then a number from 1 to 6, depending on the list you want to clear. Data Management 12 Technology Appendix Page 5 • To enter data, use the cursor keys to move to the list you want. Type a value, then press ENTER . For example, the numbers 1 to 7 are shown entered in list L1. You can enter a formula for a list. For example, use list L2 to calculate the square of each number in list L1. • Move to the top of list L2. • Press 2nd , then 1 . • Press x2 , then ENTER . The squares of the numbers in list L1 will display in list L2. Create a Histogram for Ungrouped Data The ages of 20 children in a dance class are 4, 5, 7, 4, 6, 9, 8, 5, 6, 8, 7, 9, 4, 5, 8, 6, 9, 7, 8, and 6. • Clear all lists. Enter the ages into list L1. • Press 2nd , then Y= to access the STAT PLOTS screen, [STAT PLOT]. • If any plots are On, select 4:PlotsOff and press ENTER . Return to the STAT PLOTS screen. • Select 1:Plot1. • Scroll to On and press ENTER . • Scroll to the third selection under Type (the histogram), and press ENTER . • Set Xlist to L1. • Set Freq to 1. The settings should appear as shown. • Press ENTER ZOOM and select 9:ZoomStat. The histogram will display. • Press WINDOW . • Adjust the window settings as shown. • Press GRAPH . The histogram will display. • Press TRACE . • Use the cursor keys to inspect the data values. You can change the histogram to display age groups of two years rather than one year. Data Management 12 Technology Appendix Page 6 • Press WINDOW . • Change Xmin to 2, Xmax to 12, Xscl to 2, and Ymax to 10. • Press GRAPH , then TRACE . Note that the interval width for the age data is now 2 years rather than 1 year. Create a Histogram for Grouped Data Sometimes data are already grouped, with a data column and a frequency column. For example, consider shoe size data for a sample of 20 customers as shown. Shoe size appears in list L1 and frequency appears in list L2. • Clear all lists. Enter the data into the lists as shown. • Press 2nd , then Y= to access the STAT PLOTS screen, [STAT PLOT]. • If any plots are ON, select 4:PlotsOff and press ENTER . Return to the STAT PLOTS screen. • Select 1:Plot1. • Scroll to ON and press ENTER . • Scroll to the third selection under Type (the histogram), and press ENTER . • Set Xlist to L1. • Set Freq to L2. The settings should appear as shown. • Press ZOOM and select 9:ZoomStat. The histogram will display. • Press WINDOW . • Adjust the window settings as shown. • Press GRAPH . • Press TRACE , and use the cursor keys to inspect the data values. Data Management 12 Technology Appendix Page 7 Create a Frequency Polygon You can plot a frequency polygon over a histogram. Refer to the shoe size histogram in the previous section. • Add the midpoint of each shoe size range in list L3, as shown. • Press 2nd , then Y= to access the [STAT PLOT] screen. • Select 2:Plot2. • Scroll to ON and press ENTER . • Scroll to the second selection under Type (the line scatter plot), and press ENTER . • Set Xlist to L3. • Set Ylist to L2. The settings should appear as shown. • Press GRAPH . The frequency polygon will appear over the histogram. • Press TRACE , and use the cursor keys to inspect the data values. Calculate Factorials, Permutations, and Combinations Suppose that you want to calculate 5! • Press 5 . • Press MATH . • Use the cursor keys to move to the probability menu [PRB]. • Select 4:!. • Press ENTER . The value of 5! will display as 120. Suppose that you want to calculate 7P3. • Press 7 . • Press MATH . • Use the cursor keys to move to the probability menu [PRB]. • Select 2:nPr and press ENTER . • Press 3 . The value of 7P3 will display as 210. Suppose that you want to calculate 10C2. Data Management 12 Technology Appendix Page 8 • Enter 1 0 . • Press MATH . • Use the cursor keys to move to the probability menu [PRB]. • Select 3:nCr and press ENTER . • Press 2 . The value of 10C2 will display as 45. Calculate a Binomial Probability Distribution Suppose that a die is rolled 5 times, and the number of times that it displays a 2 is counted. Determine the binomial distribution for the number of 2s from 0 to 5. • Clear all lists. Enter the data 0 to 5 in list L1. The formula for the binomial distribution is nx x n x Cq p − . In this case, n = 5, p = 1 6 and q = 5 6 . • Move to the top of list L2. • Press 5 . • Press MATH . • Use the cursor keys to move to the probability menu [PRB]. • Select 3:nCr. • Press 2nd , then 1 to enter L1. • Press x ( 5 ÷ 6 ) ^ ( 5 – 2nd 1 ) x ( 1 ÷ 6 ) ^ 2nd 1 . The probability distribution will display as shown. Calculate a Hypergeometric Probability Distribution Suppose that 5 cards are dealt from a deck of 52. Determine the hypergeometric distribution for the number of diamonds from 0 to 5. • Clear all lists. Enter the data 0 to 5 in list L1. The formula for the hypergeometric distribution is a x na rx n r C C C × − − . In this case, n = 52, r = 5, and a = 13. • Move to the top of list L2. • Enter 1 5 . • Press MATH . • Use the cursor keys to move to the probability menu [PRB]. • Select 3:nCr. • Press 2nd , then 1 to enter L1. Data Management 12 Technology Appendix Page 9 • Press x and enter 39. • Press MATH and move to the probability menu [PRB]. • Select 3:nCr. • Press ( 5 – 2nd 1 ) . • Press ÷ and enter 52. • Press MATH and move to the probability menu [PRB]. • Select 3:nCr. • Press 5 . The probability distribution will display as shown. Use the Binomial Cumulative Function The probability of rain in Sloshville is predicted at 15% on every day for the next week. What is the probability that Sloshville will have 3 or fewer rainy days? • Press 2nd , then VARS to access the [DISTR] (distributions) menu. • Select B:binomcdf(. • Enter 7 for the number of trials, .15 for the probability of a success, and 3 for the x value. • Scroll to PASTE and press ENTER . The probability of 3 or fewer days with rain will display as about 0.988. Use the Normal Cumulative Function The mean time required to assemble a bicycle in a factory is 18 min with a standard deviation of 2.3 min. What is the probability that a given bicycle will take 25 min or more to assemble? • Press 2nd , then VARS to access the [DISTR] (distributions) menu. • Select 2:normalcdf(. • Enter 25 for the lower limit, 99999 for the upper limit (or 1E99 if you prefer), 18 for the mean (μ), and 2.3 for the standard deviation (σ). • Scroll to PASTE and press ENTER . The probability of taking 25 min or more to assemble a bicycle is about 0.0012. Data Management 12 Technology Appendix Page 10 Calculate One-Variable Statistics for a Sample A sample of 20 turnips from Anna’s garden has masses of 843 g, 721 g, 871 g, 604 g, 797 g, 928 g, 796 g, 908 g, 824 g, 927 g, 778 g, 823 g, 771 g, 843 g, 659 g, 819 g, 756 g, 586 g, 790 g, and 957 g. Determine the one-variable statistics for the sample. • Clear the lists. Enter the turnip mass data into list L1. • Press STAT . Use the cursor keys to access the [CALC] menu. • Select 1:1-Var Stats. • Enter L1 as the List. Leave the FreqList blank. • Scroll to Calculate and press ENTER . The one-variable statistics summary will display. Scroll down to view all of the statistics. The sample mean is about 800 g. The sum of the masses is 16 001 g. The sum of the squares of the masses is 12 994 351 g2 . The sample standard deviation is about 101 g. The population standard deviation is about 98 g. The number of data is 20. The minimum mass is 586 g. The first quartile is at about 764 g. The median is 808 g. The third quartile is at 857 g. The maximum mass is 957 g. Create a Scatter Plot and a Line of Best Fit The heights of 7 contestants in the school javelin throw, in centimetres, are shown in list L1. The distances thrown, in metres, are shown in list L2. Create a scatter plot and line of best fit for these data. • Clear the lists. Enter the data as shown. • Press 2nd , then Y= to access the [STAT PLOT] screen. Data Management 12 Technology Appendix Page 11 • If any plots are ON, select 4:PlotsOff and press ENTER . Return to the [STAT PLOT] screen. • Select 1:Plot1. • Scroll to ON and press ENTER . • Scroll to the first selection under Type (the scatter plot), and press ENTER . • Set Xlist to L1. • Set Freq to L2. The settings should appear as shown. • Press ZOOM and select 9:ZoomStat. The scatter plot will display. • Press TRACE , and use the cursor keys to inspect the data values. Add a linear regression line with the correlation coefficient. • Press 2nd , then 0 to access the [CATALOG]. • Press ALPHA , then x–1 to access D. • Scroll down to DiagnosticOn. Press ENTER twice. This will turn on the correlation coefficient. • Press STAT . Use the cursor keys to access the [CALC] menu. • Select 4:LineReg(ax+b). • Select L1 for the Xlist and L2 for the Ylist. Leave the FreqList blank. • Move to Store RegEQ:. • Press VARS , and cursor to Y-VARS. • Select 1:Function..., then 1:Y1. • Scroll to Calculate and press ENTER . The parameters for the line of best fit will display, along with the correlation coefficient. • Press Y= to see the equation of the line of best fit. • Then, press GRAPH to display the line of best fit on the scatter plot. • Press TRACE and use the cursor keys to read values from the line. Data Management 12 Technology Appendix Page 12 Generate Random Numbers The TI-83 Plus and TI-84 Plus calculators offer several random numb