10.1 Mean and standard deviation single data

Transcription

1 Masterig the Calculator usig the Sharp EL-531WH Statistics 10.1 Mea ad stadard deviatio sigle data The formula for the mea is x x The formulas for the sample stadard deviatio are s x i x (sample) x i x (populatio) Your calculator will calculate the mea ad stadard deviatio for you (the populatio stadard deviatio or the sample stadard deviatio 1 i data calculatios you will usually use the sample stadard deviatio.) O the Sharp EL-531 WH ad s for sigle data are foud by pressig. The positio of keys eeded are show o the diagram below. (key for eterig bivariate data or frequecies) iput key (Key for sum of observatios, sum of observatios squared, ad umber of observatios) To fid the mea ad stadard deviatio,

2 28 Masterig the Calculator usig the Sharp EL-531WH firstly you must access the statistics mode of the calculator by usig the keys followed by ad STAT 0 will appear o the scree. Note that oce you are i the statistics mode, the keys show i gree are active. Make sure you ca locate them. IMPORTANT: Before startig ay computatios always clear the statistic s memories usig I will use the data set A ( 5, 2, 3, 4, 11) to demostrate the use of the calculator. Note that I have show the use of the key where ecessary. Step 1: Iput the observatios. Use the key to iput data (o eed to press or ). Step 2: Check that the correct umber of observatios have bee iputted. The scree should show DATA SET 5. Or press The display should read 5. Press the gives x 3 Press gives x Press gives x Note: to clear stat data, just press or Step 3: To display the mea press ad the display should read 3 Step 4: Display the stadard deviatio (assume the data set is a sample) press the display should read ad

3 Masterig the Calculator usig the Sharp EL-531WH 29 Example Use your calculator to fid the mea, stadard deviatio ad variace for data set B: 18, 1, 3, 9, 20. (the variace is the square of the stadard deviatio) After you are i the statistics mode ad cleared the statistics memories ad exted the umber the keystrokes required are: ad the display will read 3. ad the display will read ad the display will read This is the variace s 2 The mea is 3, the stadard deviatio is ad the variace is You ca also accesses a umber of extra statistical fuctios. x x 15 5 If you have made a error with iputtig your data you ca correct it by goig back to the data. For example, you iput 4, 5, 60, 7, 9 ad you meat to iput 6 istead of 60. Go to the data o. 3, the press. You ow have the correct data. I the example below, the progressive calculatios are show simply to give you some uderstadig of the uderlyig processes you should do oe or two examples i detail ad the check them by calculator.

4 30 Masterig the Calculator usig the Sharp EL-531WH 10.2 Mea ad stadard deviatio of frequecy distributio Give below is the frequecy table for the weights (kg) of a radom sample of 30 first year uiversity female studets. Fid the stadard deviatio, the variace ad the mea. Graduate s weight (kg) Frequecy Cumulative frequecy The calculatios eeded to obtai the stadard deviatio without statistical keys for these data are: x x s 2 x i x i Thus: s 1.2 kg ad s kg 2 x x kg 30 Note: I calculatios like the above you should carry as may decimals as possible util the fial result. The umber of decimals to be retaied at the ed depeds o the accuracy of the data values oe rule of thumb is to have oe more decimal tha i the origial data. Notice how the frequecies were used i the above calculatio. The calculator usage ow has a small modificatio because we have bee give the frequecies for the variable values. (There is o eed to iput each sigle observatio.) You eed to use the key for imputtig frequecies: Press: (for sigle variate stats)

5 Masterig the Calculator usig the Sharp EL-531WH 31 the iput the data usig the key to separate the data poits ad the frequecies. To fid the mea, stadard deviatio ad variace press ad the display should read ad the display should read ad the display should read Thus, as expected s 1.2 kg, s kg 2 ad x 61.8 kg Exercise 6 Fid the mea, stadard deviatio ad variace of (a) The aual raifall data for the years Year Rai (mm) Year Rai (mm)

6 32 Masterig the Calculator usig the Sharp EL-531WH (b) The sample of sail foot legths Sail foot legth (cm) Aswers: (a) Raifall statistics mea: x mm stadard deviatio: s mm (sample stadard deviatio) variace: s mm 2 (b) Sail statistics mea: x 3.4 cm stadard deviatio: s 0.70 cm variace: s cm 2