HP 12C Financial 12C Standard Deviation, worked, sample, x-value, y-value, x-value, x-value, y-value, 4,820.59, estimate, 4,463.00, 21,714.29, population, Page: 96 of

96 Section 6: Statistics FunctionsStandard Deviation

Pressing gv calculates the standard deviation of the x-values (sx) and of the y-values (sy). (The standard deviation of a set of data is a measure of the dispersion around the mean.) The standard deviation of the x-values appears in the display

after gv is pressed; to display the standard deviation of the y-values, press ~.

Example: To calculate the standard deviations of the x-values and of the y-values from the preceding example:

Keystrokes	Display
gv	4,820.59	Standard deviation of sales.
~	6.03	Standard deviation of hours
		worked.

The formulas used in the hp 12c platinum for calculating sx and sy give best estimates of the population standard deviation based on a sample of the population. Thus, current statistical convention calls them sample standard deviations. So we have assumed that the seven salespersons are a sample of the population of all salespersons, and our formulas derive best estimates of the population from the sample.

What if the seven salespersons constituted the whole population of salespersons. Then we wouldn’t need to estimate the population standard deviation. We can find the true population standard deviation (σ) when the data set equals the total population, using the following keystrokes.*

Keystrokes	Display
gÖ	21,714.29	Mean (dollars)
_	8.00	Number of entries + 1.
gv	4,463.00	σx
~	5.58	σy

*It turns out that if you sum the mean of the population into the set itself and find the new s,

computed using the formulas on page 257, that s will be the population standard deviation, σ, of the original set.

File name: hp 12c pt_user's guide_English_HDPMF123E27	Page: 96 of 275
Printed Date: 2005/8/1	Dimension: 14.8 cm x 21 cm