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Tech 1: DESCRIPTIVE STATISTICS with TI-83 (prepared by Mrs. Krystyna Karminska- Makagon) I. One variable statistics Problems: Given a set of data. 1. Find the mean, median, standard deviation, the first and the third quartile, and the range. 2. Find the box graph and the histogram. Example : the following exercise comes from the textbook Elementary Statistics by Mario Triola, the seventh edition. “The amounts of time spent on paperwork in one day were obtained from a sample of office managers with the results given below (based on data from Adia Personal Services): 3.7 2.9 3.4 0.0 1.5 1.8 2.3 2.4 1.0 2.0 4.4 2.0 4.5 0.0 1.7 4.4 3.3 2.4 2.1 2.1” Solution: First, we will make a list of data. 1. (If you do this the first time press STAT then 5: set up the editor; and then ENTER) 2. Press STAT, ENTER to start editing your list. Type in your data. Press ENTER after every entry. Data will be listed under L 1 . Press 2 nd QUIT when done. Next we will sort the list in ascending order. Press STAT, 2:SortA to display the command on the home screen. Press 2nd, 1 to write L1 (this is a name of the list of your data). Press ENTER. The calculator will answer: “done”. Go to STAT, EDIT to see the list. Now we can obtain the statistics of the sample: Press STAT, highlight CALC, then choose 1: one-variable statistics. Follow with ENTER. You will see on the screen the following: f8e5 x =2.395 (the mean) x=47.9 (sum of all data) x 2 =146.53 (sum of all squares) Sx=1.293902705 (sample standard deviation) Sx 2 = ( (x - f8e5 x) 2 )/(n-1) σ x=1.261140357 (“population” standard deviation) σ x 2 = ( (x - f8e5 x) 2 )/n n=20 (sample size) The down arrow indicates that there is more to read on. Scroll the screen by pressing Down Arrowa few times. You’ll see: minX=0 (the minimum) Q 1 =1.75 (the first quartile) Med=2.2 (the median: the second quartile)
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Q 3 =3.35 (the third quartile) maxX=4.5 (the maximum) The range can be found by subtracting the minimum from the maximum value. The last five numbers above represent five number summary needed to draw a box graph. Now we can obtain the graphs : the illustrations of our data set. First, make sure that all graphs in the area “Y=” are either erased or unselected. We are going to draw two graphs. A . The box graph : (“Box-and-whiskers” graph) Let’s find the box plot for our sample. Press 2nd, then “Y=” to open STAT PLOTS menu. Press 1 to choose plot 1. Press ENTER to turn it on. Press Down Arrow, then Right Arrow (three or four times) to choose a type of the graph. You may choose either the first box, or the second one. The difference will occur if your sample contains any “outliers” (the values that significantly differ from the other data). The first box will display the outliers as separate points. The second box will display the whiskers, which is a line connecting minimum and maximum value. Highlight the box of your choice, press ENTER. Ready to graph? Press ZOOM and 9 for ZoomStat. Press TRACE
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