The HP 20s calculates the mean, standard deviation, n, sum, and sum of the squares of xdata. For ydata, it calculates the mean and standard deviation, sum, and sum of the squares. The HP 20s also calculates the sum of the products of x and y data.
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HP 20s Calculator  Mean, Standard Deviation, and Summation Statistics
Calculator symbol key
The procedures in this document use the following text to represent symbol keys:
Key

Description

Text Representation


Right shift key

RS


Leftshift key

LS


Divide

divide


Accumulates statistical data

SUM+


Arithmetic mean (average) of the xvalues

xy


Square root

SQRT


Square root key

SQx


Mean of the xvalues weighted by the yvalues

xw

Example of calculating the mean, standard deviation, and root mean square
A yacht captain wants to determine how long it takes to change a sail. She randomly chooses six members of her crew, observes them as they carry out the sail change, and records the number of minutes required: 4.5, 4, 2, 3.25, 3.5, 3.75.
Calculate the mean and standard deviation of the times. Also, calculate the root mean square, using the formula in Figure 1.
Figure : Formula for calculating the root mean square
Keys

Display

Description

Press RS, then CLSUM

0.0000

Clears the statistical registers

Press 4.5, then SUM+

1.0000

Enters the first time

Press 4, then SUM+

2.0000
 
Press 2, then SUM+

3.0000
 
Press 3.25, then SUM+

4.0000
 
Press 3.5, then SUM+

5.0000
 
Press 3.75, then SUM+

6.0000
 
Press RS, then xy

3.5000

Calculates the mean

Press RS, then Sx,Sy

0.8515

Calculates the standard deviation

Press RCL, then 7

77.1250

Displays the sum of squares of xdata

Press divide, RCL, then 4

6.0000

Displays n

Press =, then SQx

3.5853

Calculates the root mean square

Calculating the population standard deviation
The standard deviations calculated by entering RS, Sx,Sy, RS, Sx,Sy, LS, then SWAP are the sample standard deviations. They assume that the data is a sampling of a larger, complete set of data. If the data constitutes the entire population of data, the true population standard deviation can be calculated by calculating the mean of the original data, adding the mean to the statistical data using SUM+, and then calculating the standard deviation. For twovariable statistics, after calculating the mean of the original data, press LS, then SWAP to put the data in the proper order (mean average of the yvalues in the display), then press SUM+
Example of calculating population standard deviation
The coach has four new players on the team with heights of 193, 182, 177, and 185 centimeters and weights of 90, 81, 83, and 77 kilograms. Find the mean and population standard deviations of their heights and weights.
Keys

Display

Description

Press RS, then CLSUM

0.0000

Clears the statistical registers.

Press 193, INPUT, 90, then SUM+

1.0000

Enters height and weight of player 1.

Press 182, INPUT, 81, then SUM+

2.0000

Enters height and weight of player 2.

Press 177, INPUT, 83, SUM+

3.0000

Enters height and weight of player 3.

Press 185, INPUT, 77, SUM+

4.0000

Enters height and weight of player 4.

Press RS, then xy

184.2500

Calculates mean of heights (x).

Press LS, then SWAP

82.7500

Displays mean of weights (y).

Press SUM+

5.0000

Adds means to data. (Data must be in x, y order with the y in the display).

Press RS, then SxSy

5.8041

Calculates population standard deviation for heights (x).

Press LS, then SWAP

4.7104

Displays population standard deviation for weights (y).

Weighted mean
An example of weighted mean is x_{1}, x_{2}, ..., x_{n} occurring with weights y_{1}, y_{2}, ..., y_{n}. To calculate weighted mean:

Use SUM+ to enter the data as x,ypairs. The yvalues are the weights of the xvalues.

Press RS, then xw
Example of calculating weighted mean
A manufacturing company purchases a certain part four times a year. Last year's purchases were:
Price/Part

$4.25

$4.60

$4.70

$4.10

Number of parts

250

800

900

1000

Calculate the average price per part.
Keys

Display

Description

Press RS, then CLSUM

0.0000

Clears the statistical registers.

Press 4.25, INPUT, 250, then SUM+

1.0000
 
Press 4.6, INPUT, 800, then SUM+

2.0000
 
Press 4.7, INPUT, 900, then SUM+

3.0000
 
Press 4.1, INPUT, 1000, then SUM+

4.0000

Enters the data and their weights.

Press RS, then xw

4.4314

Calculates weighted mean (average part price).

Figure : Statistical formulas
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