Download Some Excel Statistical Functions

Some Excel Statistical Functions
Excel’s statistical functions are built-in formulas that carry out certain calculations. To use them, enter the
appropriate formula in a cell and give the formula all the arguments it requires. You may already be familiar with
some of these functions from accounting or finance courses, where you may have learned to calculate present
values, payments on a debt at a given interest rate, or the sum of a column of figures.
For simple descriptive statistics, Excel provides formulas to calculate the mean, median, mode, variance, standard
deviation and several other measures. Following is a list of functions with their “arguments,” or information that
must be entered to get an answer. To use these formulas, you must begin by entering an = in the cell.
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AVERAGE(individual numbers or data range) calculates the arithmetic mean
o Examples:
ƒ =AVERAGE(6, 2, 8, 12) will display 7
ƒ =AVERAGE(C6:C22) will display the arithmetic mean of the numbers in column C rows
6 through 22
MEDIAN(individual numbers or data range) calculates the median
o Examples:
ƒ =MEDIAN(6, 2, 8, 12) will display 7
ƒ =MEDIAN(C6: C22) will display the median of the numbers in this range regardless of
the order in which the numbers are entered in the spreadsheet
MODE(individual numbers or data range) finds the mode
STDEV(individual numbers or data range) displays the sample standard deviation
VAR(individual numbers or data range) displays the sample variance
o In these cases, division is by n – 1 or one less than the size of the data set
o Examples: ƒ =STDEV(0,10,5,20,15) displays 7.905694 ƒ =VAR(0, 10, 5, 20, 15) displays 62.5 ƒ If the numbers 0, 10, 5, 20, 15 are entered into cells B2 to B6, =STDEV(B2:B6) displays
7.905694 ƒ
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If the numbers 0, 10, 5, 20, 15 are entered into cells B2 to B6, =VAR(B2:B6) displays
62.5
STDEVP(individual numbers or data range) calculates a population standard deviation
VARP(numbers or range) calculates a population variance
o In these cases, division is by the size of the data set
o Examples: ƒ STDEVP(B2:B6) with data as above displays 7.071068 ƒ VARP(B2:B6) with data as above displays 50
For probability functions, Excel provides two types of functions. With ___DIST functions, you enter an x value and
the spreadsheet displays a probability. With ___INV functions, you enter a probability and the spreadsheet displays
an x value.
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Normal Probabilities:
o NORMDIST(x0, μ, σ, CUMULATIVE)
ƒ If “CUMULATIVE” has value “TRUE” this formula returns P(x ≤ x0) for the normal
distribution with given μ, σ
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=normdist(20,25,5,true) = 0.1587 is the probability of values less than or equal to 20 on a
normal distribution with μ = 25 and σ = 5
NORMINV(PROBABILITY, μ, σ)
ƒ this formula returns the x0 such that P(x ≤ x0) has the probability entered in the formula
ƒ NORMINV(.975, 200, 20) = 239.2; on a normal distribution with mean 200 and standard
deviation 20, .975 of the distribution is less than 239.2
NORMSDIST(z0): returns P(z ≤ z0)
NORMSINV(PROBABILITY): returns z0 such that P(z ≤ z0) has the given probability
To work repeated problems, create a specialized spreadsheet: for example, in Cell A4 enter Prob
(x <= x0); in cell B4, enter =NORMDIST(B6, B7, B8, TRUE). In A5 enter Prob( x > x0) and in
B5 enter =1-B4). Then enter an x value in B6, mean in B7, and standard deviation in B8. You
will of course want to enter labels in A6 to A8.
t Distribution Probabilities:
o TDIST(t, degrees of freedom, tails)
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t=
x − μ0
sx
or other t formulas which we will
encounter
degrees of freedom will depend on the problem; in simple hypothesis tests, we have df =
n–1
ƒ “tails” takes the value 1 or 2, depending on whether it’s a one-tailed or two-tailed test
ƒ the result of tdist is the probability of a t value as great as that actually obtained; it is the
area under the graph of the t distribution beyond the calculated value of t. If we specify 1
for “tails,” it is the area in one tail beyond the calculated value; if we specify 2 for “tails,”
it is the area in the tails beyond ±t.
ƒ in hypothesis testing, the result of the TDIST formula is the p-value of the test.
ƒ TDIST(3.15, 9, 1) = 0.00362; TDIST(1.93, 22, 2) = 0.0666
TINV(probability, degrees of freedom)
ƒ returns a t value with the specified probability split between the two tails
ƒ used for finding t values for use with confidence intervals
• TINV(0.05, 22) = 2.073875 gives the t value that would be used for calculating
a 95% confidence interval with a sample of n = 23
ƒ or for finding critical t values: for a two-tailed test, enter the significance level for
“probability”; for a two-tailed test, enter twice the significance level for “probability”
• TINV(0.01, 44) = 2.692286 is the critical value for a two-tailed test at 1%
significance with 44 degrees of freedom
• TINV(0.1, 26) = 1.705616 is the critical value for an upper one-tailed test at 5%
significance with 26 degrees of freedom; −1.705616 is the critical value for a
lower one-tailed test with same conditions
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t is a calculated value from the formula