Statistical Functions Part One
COUNTIFS
Returns the count of cells that meet criteria in multiple ranges.
B
Returns the probability of a sample with binomial distribution.
Syntax
B(Trials; SP; T1; T2)
Trials is the number of independent trials.
SP: ймовірність успіху кожного випробування.
T1 defines the lower limit for the number of trials.
T2 (optional) defines the upper limit for the number of trials.
Приклад
What is the probability with ten throws of the dice, that a six will come up exactly twice? The probability of a six (or any other number) is 1/6. The following formula combines these factors:
=B(10;1/6;2) returns a probability of 29%.
BETA.DIST
Повертає бета-функцію.
Syntax
BETA.DIST(Number; Alpha; Beta; Cumulative; Start; End)
Number (required) is the value between Start and End at which to evaluate the function.
Alpha (required) is a parameter to the distribution.
Beta (required) is a parameter to the distribution.
Інтегральне (обов'язковий параметр): може набувати значення 0 або False для обчислення функції щільності розподілу. Якщо цей параметр має інше значення або True, то обчислюється інтегральна функція розподілу.
Start (optional) is the lower bound for Number.
End (optional) is the upper bound for Number.
In the LibreOffice Calc functions, parameters marked as "optional" can be left out only when no parameter follows. For example, in a function with four parameters, where the last two parameters are marked as "optional", you can leave out parameter 4 or parameters 3 and 4, but you cannot leave out parameter 3 alone.
Приклади
=BETA.DIST(2;8;10;1;1;3) returns the value 0.6854706
=BETA.DIST(2;8;10;0;1;3) returns the value 1.4837646
BETA.INV
Повертає обернену інтегральну функцію щільності бета-розподілу.
Syntax
BETA.INV(Number; Alpha; Beta; Start; End)
Number is the value between Start and End at which to evaluate the function.
Alpha is a parameter to the distribution.
Beta is a parameter to the distribution.
Start (optional) is the lower bound for Number.
End (optional) is the upper bound for Number.
In the LibreOffice Calc functions, parameters marked as "optional" can be left out only when no parameter follows. For example, in a function with four parameters, where the last two parameters are marked as "optional", you can leave out parameter 4 or parameters 3 and 4, but you cannot leave out parameter 3 alone.
Приклад
=BETA.INV(0.5;5;10) returns the value 0.3257511553.
BETADIST
Повертає бета-функцію.
Syntax
BETADIST(Number; Alpha; Beta; Start; End; Cumulative)
Number is the value between Start and End at which to evaluate the function.
Alpha is a parameter to the distribution.
Beta is a parameter to the distribution.
Start (optional) is the lower bound for Number.
End (optional) is the upper bound for Number.
Інтегральне (необов'язковий параметр): може приймати значення 0 або FALSE; в цьому випадку обчислюється функція щільності розподілу ймовірностей. Якщо цей параметр має відмінне від нуля значення, значення TRUE або він пропущений, то обчислюється інтегральна функція розподілу.
In the LibreOffice Calc functions, parameters marked as "optional" can be left out only when no parameter follows. For example, in a function with four parameters, where the last two parameters are marked as "optional", you can leave out parameter 4 or parameters 3 and 4, but you cannot leave out parameter 3 alone.
Приклад
=BETADIST(0.75;3;4) returns the value 0.96.
BETAINV
Повертає обернену інтегральну функцію щільності бета-розподілу.
Syntax
BETAINV(Number; Alpha; Beta; Start; End)
Number is the value between Start and End at which to evaluate the function.
Alpha is a parameter to the distribution.
Beta is a parameter to the distribution.
Start (optional) is the lower bound for Number.
End (optional) is the upper bound for Number.
In the LibreOffice Calc functions, parameters marked as "optional" can be left out only when no parameter follows. For example, in a function with four parameters, where the last two parameters are marked as "optional", you can leave out parameter 4 or parameters 3 and 4, but you cannot leave out parameter 3 alone.
Приклад
=BETAINV(0.5;5;10) returns the value 0.33.
BINOM.DIST
Returns the individual term binomial distribution probability.
Syntax
BINOM.DIST(X; Trials; SP; C)
X is the number of successes in a set of trials.
Trials is the number of independent trials.
SP: ймовірність успіху кожного випробування.
C = 0 calculates the probability of a single event and C = 1 calculates the cumulative probability.
Приклад
=BINOM.DIST(A1;12;0.5;0) shows (if the values 0 to 12 are entered in A1) the probabilities for 12 flips of a coin that Heads will come up exactly the number of times entered in A1.
=BINOM.DIST(A1;12;0.5;1) shows the cumulative probabilities for the same series. For example, if A1 = 4, the cumulative probability of the series is 0, 1, 2, 3 or 4 times Heads (non-exclusive OR).
BINOM.INV
Returns the smallest value for which the cumulative binomial distribution is greater than or equal to a criterion value.
Syntax
BINOM.INV(Trials; SP; Alpha)
Trials The total number of trials.
SP: ймовірність успіху кожного випробування.
Alpha The border probability that is attained or exceeded.
Приклад
=BINOM.INV(8;0.6;0.9) returns 7, the smallest value for which the cumulative binomial distribution is greater than or equal to a criterion value.
BINOMDIST
Returns the individual term binomial distribution probability.
Syntax
BINOMDIST(X; Trials; SP; C)
X is the number of successes in a set of trials.
Trials is the number of independent trials.
SP: ймовірність успіху кожного випробування.
C = 0 calculates the probability of a single event and C = 1 calculates the cumulative probability.
Приклад
=BINOMDIST(A1;12;0.5;0) shows (if the values 0 to 12 are entered in A1) the probabilities for 12 flips of a coin that Heads will come up exactly the number of times entered in A1.
=BINOMDIST(A1;12;0.5;1) shows the cumulative probabilities for the same series. For example, if A1 = 4, the cumulative probability of the series is 0, 1, 2, 3 or 4 times Heads (non-exclusive OR).
CHIDIST
Returns the probability value from the indicated Chi square that a hypothesis is confirmed. CHIDIST compares the Chi square value to be given for a random sample that is calculated from the sum of (observed value-expected value)^2/expected value for all values with the theoretical Chi square distribution and determines from this the probability of error for the hypothesis to be tested.
The probability determined by CHIDIST can also be determined by CHITEST.
Syntax
CHIDIST(Number; DegreesFreedom)
Number is the chi-square value of the random sample used to determine the error probability.
DegreesFreedom are the degrees of freedom of the experiment.
Приклад
=CHIDIST(13.27; 5) equals 0.02.
If the Chi square value of the random sample is 13.27 and if the experiment has 5 degrees of freedom, then the hypothesis is assured with a probability of error of 2%.
CHIINV
Повертає значення, обернене до односторонньої ймовірності розподілу хі-квадрат.
Syntax
CHIINV(Number; DegreesFreedom)
Number is the value of the error probability.
DegreesFreedom is the degrees of freedom of the experiment.
Приклад
A die is thrown 1020 times. The numbers on the die 1 through 6 come up 195, 151, 148, 189, 183 and 154 times (observation values). The hypothesis that the die is not fixed is to be tested.
The Chi square distribution of the random sample is determined by the formula given above. Since the expected value for a given number on the die for n throws is n times 1/6, thus 1020/6 = 170, the formula returns a Chi square value of 13.27.
If the (observed) Chi square is greater than or equal to the (theoretical) Chi square CHIINV, the hypothesis will be discarded, since the deviation between theory and experiment is too great. If the observed Chi square is less that CHIINV, the hypothesis is confirmed with the indicated probability of error.
=CHIINV(0.05;5) returns 11.07.
=CHIINV(0.02;5) returns 13.39.
If the probability of error is 5%, the die is not true. If the probability of error is 2%, there is no reason to believe it is fixed.
CHISQ.DIST
Повертає значення функції щільності розподілу ймовірності або функції інтегрального розподілу для розподілу хі-квадрат.
Syntax
CHISQ.DIST(Number; DegreesFreedom; Cumulative)
Number is the chi-square value of the random sample used to determine the error probability.
DegreesFreedom are the degrees of freedom of the experiment.
Інтегральне: може набувати значення 0 або False для обчислення функції щільності розподілу. Якщо цей параметр має інше значення або True, то обчислюється інтегральна функція розподілу.
Приклад
=CHISQ.DIST(3; 2; 0) equals 0.1115650801, the probability density function with 2 degrees of freedom, at x = 3.
=CHISQ.DIST(3; 2; 1) equals 0.7768698399, the cumulative chi-square distribution with 2 degrees of freedom, at the value x = 3.
CHISQ.DIST.RT
Returns the probability value from the indicated Chi square that a hypothesis is confirmed. CHISQ.DIST.RT compares the Chi square value to be given for a random sample that is calculated from the sum of (observed value-expected value)^2/expected value for all values with the theoretical Chi square distribution and determines from this the probability of error for the hypothesis to be tested.
The probability determined by CHISQ.DIST.RT can also be determined by CHITEST.
Syntax
CHISQ.DIST.RT(Number; DegreesFreedom)
Number is the chi-square value of the random sample used to determine the error probability.
DegreesFreedom are the degrees of freedom of the experiment.
Приклад
=CHISQ.DIST.RT(13.27; 5) equals 0.0209757694.
If the Chi square value of the random sample is 13.27 and if the experiment has 5 degrees of freedom, then the hypothesis is assured with a probability of error of 2%.
CHISQ.INV
Повертає значення, обернене до односторонньої ймовірності розподілу хі-квадрат.
Syntax
CHISQ.INV(Probability; DegreesFreedom)
Ймовірність: значення ймовірності, для якої потрібно обчислити обернений розподіл хі-квадрат.
Degrees Of Freedom is the degrees of freedom for the chi-square function.
Приклад
=CHISQ.INV(0,5;1) returns 0.4549364231.
CHISQ.INV.RT
Повертає значення, обернене до односторонньої ймовірності розподілу хі-квадрат.
Syntax
CHISQ.INV.RT(Number; DegreesFreedom)
Number is the value of the error probability.
DegreesFreedom is the degrees of freedom of the experiment.
Приклад
A die is thrown 1020 times. The numbers on the die 1 through 6 come up 195, 151, 148, 189, 183 and 154 times (observation values). The hypothesis that the die is not fixed is to be tested.
The Chi square distribution of the random sample is determined by the formula given above. Since the expected value for a given number on the die for n throws is n times 1/6, thus 1020/6 = 170, the formula returns a Chi square value of 13.27.
If the (observed) Chi square is greater than or equal to the (theoretical) Chi square CHIINV, the hypothesis will be discarded, since the deviation between theory and experiment is too great. If the observed Chi square is less that CHIINV, the hypothesis is confirmed with the indicated probability of error.
=CHISQ.INV.RT(0.05;5) returns 11.0704976935.
=CHISQ.INV.RT(0.02;5) returns 13.388222599.
If the probability of error is 5%, the die is not true. If the probability of error is 2%, there is no reason to believe it is fixed.
CHISQ.TEST
Returns the probability of a deviance from a random distribution of two test series based on the chi-squared test for independence. CHISQ.TEST returns the chi-squared distribution of the data.
The probability determined by CHISQ.TEST can also be determined with CHISQ.DIST, in which case the Chi square of the random sample must then be passed as a parameter instead of the data row.
Syntax
CHISQ.TEST(DataB; DataE)
DataB is the array of the observations.
DataE is the range of the expected values.
Приклад
|
Data_B (observed) |
Data_E (expected) |
|
|
1 |
195 |
170 |
|
2 |
151 |
170 |
|
3 |
148 |
170 |
|
4 |
189 |
170 |
|
5 |
183 |
170 |
|
6 |
154 |
170 |
=CHISQ.TEST(A1:A6;B1:B6) equals 0.0209708029. This is the probability which suffices the observed data of the theoretical Chi-square distribution.
CHISQDIST
Повертає значення функції щільності розподілу ймовірності або функції інтегрального розподілу для розподілу хі-квадрат.
Syntax
CHISQDIST(Number; Degrees Of Freedom; Cumulative)
Число: число, для якого обчислюється функція.
Degrees Of Freedom is the degrees of freedom for the chi-square function.
Інтегральний (необов'язковий параметр): у разі значення 0 або FALSE обчислюється функція щільності розподілу ймовірностей. Якщо цей параметр має відмінне від нуля значення, значення TRUE або пропущений, то обчислюється інтегральна функція розподілу.
CHISQINV
Повертає обернене значення CHISQDIST.
Syntax
Ймовірність: значення ймовірності, для якої потрібно обчислити обернений розподіл хі-квадрат.
Degrees Of Freedom is the degrees of freedom for the chi-square function.
CHITEST
Returns the probability of a deviance from a random distribution of two test series based on the chi-squared test for independence. CHITEST returns the chi-squared distribution of the data.
The probability determined by CHITEST can also be determined with CHIDIST, in which case the Chi square of the random sample must then be passed as a parameter instead of the data row.
Syntax
CHITEST(DataB; DataE)
DataB is the array of the observations.
DataE is the range of the expected values.
Приклад
|
Data_B (observed) |
Data_E (expected) |
|
|
1 |
195 |
170 |
|
2 |
151 |
170 |
|
3 |
148 |
170 |
|
4 |
189 |
170 |
|
5 |
183 |
170 |
|
6 |
154 |
170 |
=CHITEST(A1:A6;B1:B6) equals 0.02. This is the probability which suffices the observed data of the theoretical Chi-square distribution.
COUNT
Counts how many numbers are in the list of arguments. Text entries are ignored.
Syntax
COUNT(Value1; Value2; ...; Value30)
Value1; Value2, ..., Value30 are 1 to 30 values or ranges representing the values to be counted.
Приклад
The entries 2, 4, 6 and eight in the Value 1-4 fields are to be counted.
=COUNT(2;4;6;"eight") = 3. The count of numbers is therefore 3.
COUNTA
Counts how many values are in the list of arguments. Text entries are also counted, even when they contain an empty string of length 0. If an argument is an array or reference, empty cells within the array or reference are ignored.
Syntax
COUNTA(Value1; Value2; ...; Value30)
Value1; Value2, ..., Value30 are 1 to 30 arguments representing the values to be counted.
Приклад
The entries 2, 4, 6 and eight in the Value 1-4 fields are to be counted.
=COUNTA(2;4;6;"eight") = 4. The count of values is therefore 4.
COUNTBLANK
Returns the number of empty cells.
Syntax
COUNTBLANK(Range)
Returns the number of empty cells in the cell range Range.
Приклад
=COUNTBLANK(A1:B2) returns 4 if cells A1, A2, B1, and B2 are all empty.
COUNTIF
Returns the number of cells that meet with certain criteria within a cell range.
Syntax
COUNTIF(Range; Criteria)
Range is the range to which the criteria are to be applied.
Criteria indicates the criteria in the form of a number, an expression or a character string. These criteria determine which cells are counted. If regular expressions are enabled in calculation options you may also enter a search text in the form of a regular expression, e.g. b.* for all cells that begin with b. If wildcards are enabled in calculation options you may enter a search text with wildcards, e.g. b* for all cells that begin with b. You may also indicate a cell address that contains the search criterion. If you search for literal text, enclose the text in double quotes.
Приклад
A1:A10 is a cell range containing the numbers 2000 to 2009. Cell B1 contains the number 2006. In cell B2, you enter a formula:
=COUNTIF(A1:A10;2006) - this returns 1.
=COUNTIF(A1:A10;B1) - this returns 1.
=COUNTIF(A1:A10;">=2006") - this returns 4.
=COUNTIF(A1:A10;"<"&B1) - when B1 contains 2006, this returns 6.
=COUNTIF(A1:A10;C2) where cell C2 contains the text >2006 counts the number of cells in the range A1:A10 which are >2006.
To count only negative numbers: =COUNTIF(A1:A10;"<0")
EXPON.DIST
Повертає експоненційний розподіл.
Syntax
EXPON.DIST(Number; Lambda; C)
Number is the value of the function.
Lambda is the parameter value.
C: логічне значення, яке визначає формат функції. У разі C = 0 розраховується функція щільності, а в разі C = 1 розраховується розподіл.
Приклад
=EXPON.DIST(3;0.5;1) returns 0.7768698399.
EXPONDIST
Повертає експоненційний розподіл.
Syntax
EXPONDIST(Number; Lambda; C)
Number is the value of the function.
Lambda is the parameter value.
C: логічне значення, яке визначає формат функції. У разі C = 0 розраховується функція щільності, а в разі C = 1 розраховується розподіл.
Приклад
=EXPONDIST(3;0.5;1) returns 0.78.
INTERCEPT
Calculates the point at which a line will intersect the y-values by using known x-values and y-values.
Syntax
INTERCEPT(DataY; DataX)
DataY is the dependent set of observations or data.
DataX is the independent set of observations or data.
Names, arrays or references containing numbers must be used here. Numbers can also be entered directly.
Приклад
To calculate the intercept, use cells D3:D9 as the y value and C3:C9 as the x value from the example spreadsheet. Input will be as follows:
=INTERCEPT(D3:D9;C3:C9) = 2.15.
RSQ
Returns the square of the Pearson correlation coefficient based on the given values. RSQ (also called determination coefficient) is a measure for the accuracy of an adjustment and can be used to produce a regression analysis.
Syntax
RSQ(DataY; DataX)
DataY is an array or range of data points.
DataX is an array or range of data points.
Приклад
=RSQ(A1:A20;B1:B20) calculates the determination coefficient for both data sets in columns A and B.