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1 HP 1C Statistics - average ad stadard deviatio Average ad stadard deviatio cocepts HP1C average ad stadard deviatio Practice calculatig averages ad stadard deviatios with oe or two variables

2 HP 1C Statistics - average ad stadard deviatio Average ad stadard deviatio cocepts Statistics ca be uderstood as a set of tools ivolvig the study of methods ad procedures used for collectig, classifyig, ad aalyzig data. Statistical tools also offer the meas for makig scietific ifereces from such resultig summarized data. Two of these tools are the Average ad the Stadard Deviatio. Give a set of collected data, the average is defied as a measure of cetral tedecy ad is the most commoly used. Its value is computed as the sum of all data poits divided by the umber of data poits icluded. The stadard deviatio is oe idex of variability used to characterize the dispersio amog the data i a give populatio or a sample. It is measures dispersio aroud the average. The property of the stadard deviatio is such that whe the uderlyig data is ormally distributed, approximately 68% of all values will lie withi oe stadard deviatio o either side of the mea, ad approximately 95% of all values will lie withi two stadard deviatios o either side of the mea. This has applicatio to may fields, particularly whe tryig to decide if a observed value is uusual by beig sigificatly differet from the mea. HP1C average ad stadard deviatio O the HP1C, statistics data are stored as a set of summatios resultig from the origially collected data. The collected data set must be typed i prior to use ay statistics features available i the HP1C because all values produced by these statistics tools deped o them. The HP1C memory orgaizatio allows the study of statistic data orgaized as oe- or two-variable samples. As a geeral procedure, data is always collected as a pair of umbers, or (x,y) values, ad the HP1C computes the followig summatios: x y ( x ) ( y ) ( y ) x Figure 1 With these values updated ad stored i memory, the HP1C computes the average ( x, y ) for each variable with the followig expressios: x x = ad y y = Figure The followig expressios are used by the HP1C to compute the stadard deviatio of a sample: ( x ) ( x ) Sx = ( 1) ad ( y ) ( y ) Sy = ( 1) Figure 3 Practice fidig average sale prices ad stadard deviatios Example 1: The sales price of the last 10 homes sold i the Parkdale commuity were: $198,000; $185,000; $05,00; $5,300; $06,700; $01,850; $00,000; $189,000; $19,100; $00,400. What is the average of these sales prices ad what is the sample stadard deviatio? Would a sales price of $40,000 be cosidered uusual i the same commuity? hp calculators - - HP 1C Statistics - average ad stadard deviatio - Versio 1.0

3 HP 1C Statistics - average ad stadard deviatio Solutio: Be sure to clear the statistics / summatio memories before startig the problem. f² Figure 4 Each etered data value causes the display to chage ad display the umber of curret etries (). Now eter each data value with _: _ Figure 5 The display represeted i Figure shows curret value of _ 0500 _ 5300 _ _ _ _ _ _ _ Figure 6 Figure 6 represets the display after the last etry. With all data already etered, all summatios are ready ad it is possible to compute both the average ad the stadard deviatio. To compute the average press: gö Figure 7 Ö is the blue fuctio o the frot, slated face of the 0 key, so g (the blue prefix key) must be pressed first. To compute the stadard deviatio, press: gv Figure 8 hp calculators HP 1C Statistics - average ad stadard deviatio - Versio 1.0

4 HP 1C Statistics - average ad stadard deviatio v is the blue fuctio o the frot, slated face of the. key. Based o these figures, approximately 68% of the prices are i the rage $00, ± $11, Approximately 95% of the prices are i the rage $00, ± ($11,189.04). The followig keystroke sequece gives the lower boudary: gö \ gv µ ~ d - Figure 9 The display shows the lower boudary. To compute higher boudary, if o operatio has bee performed after the above keystrokes, press: ~ gf + Figure 10 The display shows the higher boudary. Aswer: $40, is a uusual price for a home at the Parkdale commuity based o the last 10 sales prices. Practice with average ad stadard deviatio with two variables Example : A lad researcher wats to compute the relatioship betwee the costructed area ad the lad area of eight homes located i his eighborhood. Iitially he eeds to kow the average ad the stadard deviatio for both parameters. His measuremets allowed him to build the followig chart: Lad Area (sq yards) Costructio Area (sq yards) Lad Area (sq yards) Costructio Area (sq yards) Solutio: Be sure to clear the statistics / summatio memories before startig the problem. f² Figure 11 hp calculators HP 1C Statistics - average ad stadard deviatio - Versio 1.0

5 HP 1C Statistics - average ad stadard deviatio Each pair must be etered to add it to the statistics summatios. 310 \ 1000 _ Figure 1 The first etered value (costructio area) is computed as the y variable ad the secod value (lad area) is computed as the x variable. The display shows the umber of etries. Make sure that all data is etered: 560 \ _ 90 \ _ 3300 \ _ 080 \ 9000 _ 700 \ _ 380 \ _ 3080 \ 1000 _ To compute the average: gö Figure 13 Average lad area: 11,375 sq yards. ~ Figure 14 Figure 15 Average costructio area:,880 sq yards. To compute the stadard deviatio: gv Stadard deviatio for lad area: 1,685.0 sq yards. Figure 16 hp calculators HP 1C Statistics - average ad stadard deviatio - Versio 1.0

6 HP 1C Statistics - average ad stadard deviatio ~ Figure 17 Stadard deviatio for costructio area: sq yards. Aswer: The average lad area for this sample is 11,375 sq yards ad the stadard deviatio is 1,685.0 sq yards. For the costructio area, the average is,880 sq yards ad the stadard deviatio is sq yards. hp calculators HP 1C Statistics - average ad stadard deviatio - Versio 1.0

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