The absolute value function changes all negative numbers to positive numbers. Positive numbers and 0 are not changed.
The common notation for absolute value in mathematical writing is | | . For example, | -14 | equals 14.
ABS(number)
For number, specify a number or a column of numbers from which to calculate the absolute value.
Formula | Result |
---|---|
ABS(-23.5) | 23.5 |
ABS(0.34) | 0.34 |
The absolute value function is useful for assessing the magnitude of values (such as the bias in a measurement system and the effects of factors on a response) apart from their direction.
The combinations function calculates the number of combinations of n items chosen k at a time. A combination is a selection of objects from a group, when the order of the selection does not matter. For example, the combinations of the letters abcd taken three at a time are abc, abd, acd, bcd. The subgroups abc and bca are considered the same combination, because order does not matter.
The combinations function is used in the formula to calculate the probability of observing k events (successes) in n trials in an experiment with only two outcomes (a binomial experiment).
COMBINATIONS(number of items, number to choose)
Specify an integer or column of integers for the number of items and the number to choose. The number of items must be greater than or equal to 1, and the number to choose must be greater than or equal to 0.
A researcher conducts a study with three people, but there are ten people willing to participate. The researcher wants to know how many combinations of three people can be chosen for the study.
Formula | Result |
---|---|
COMBINATIONS(10, 3) | 120 |
The concatenate function combines two or more text columns side-by-side and stores them in a new column.
CONCATENATE(text, text, ...)
For text, specify the columns or text values to combine. Text values must be enclosed in double-quotes. Minitab treats the values in numeric columns as text characters.
A human resources assistant wants to combine a column of first names with a column of last names. The assistant enters the expression CONCATENATE(C1, " ", C2) to create a column that contains the first name, followed by a space, followed by the last name. Text values, such as the space in this example, must be enclosed in double-quotes.
C1 | C2 | C3 |
---|---|---|
First name | Last name | Name |
Sarah | Jenkins | Sarah Jenkins |
Rick | Salazar | Rick Salazar |
Jasmine | Evra | Jasmine Evra |
The exponential function calculates the value e^{x}, where e is the base of the natural log equal to approximately 2.71828 and x is the value that you enter. For example, the exponential of 5 is e^{5}, which equals about 148.413. Usually, the function y = e^{x} is called the natural exponential function.
EXP(number)
For number, specify a number or a column of numbers.
Formula | Result |
---|---|
EXP(2) | 7.38905609893 |
The exponential function is often used to model amounts (such as compound interest, radioactive decay, or population growth) that increase or decrease by a constant exponential factor.
The factorial function calculates the factorial of a nonnegative integer, n. The factorial of n is the product of all the consecutive integers from 1 to n, inclusive. The notation n! is used to represent the factorial. For example, 5! = 1* 2 * 3 * 4 * 5 = 120. By definition, 0! = 1.
FACTORIAL(number of items)
The value of number of items must be greater than or equal to 0. You can enter a column or constant. Missing values are not allowed.
Formula | Result |
---|---|
FACTORIAL(6) | 720 |
The if function chooses which of two values to return based on whether a condition is true or false.
IF(test, value if true, [value if false])
For test, specify the condition, and for value if true, specify the value to return if the condition is true. Conditions can be any numerical or logical expressions. The third argument, value if false, is optional and lets you specify a value to return if the condition is false. If you don't specify value if false, Minitab returns a missing value.
To change a column of 0's and 1's to "male" and "female", enter the expression IF(C1=1, "male", "female").
C1 | C2 |
---|---|
Expression | |
0 | female |
1 | male |
0 | female |
1 | male |
0 | female |
The log base 10 function calculates the exponent to which 10 must be raised to equal a given number. For example, 10^{2} = 100, so LOGTEN(100) = 2. LOGTEN is defined only for positive numbers. When you multiply a number by 10, you increase its log by 1. When you divide a number by 10, you decrease its log by 1.
LOGTEN(number)
For number, specify a number or a column of numbers. Minitab computes the value x such that 10^{x} = the number. If you enter 0 or a negative number, Minitab stores a missing value *.
Formula | Result |
---|---|
LOGTEN(0.01) | -2 |
LOGTEN(0.1) | -1 |
LOGTEN(1) | 0 |
LOGTEN(10) | 1 |
LOGTEN(100) | 2 |
The maximum function identifies the largest value in a column. The minimum function identifies the smallest value in a column.
Function | Syntax |
---|---|
Maximum | MAX(number) |
Minimum | MIN(number) |
For number, specify a column of numbers.
Columns | Formula | Result |
---|---|---|
C1 contains 6, 3, 15 | MAX(C1) | 15 |
C1 contains 22, 3, 7 | MIN(C1) | 3 |
The mean function calculates the arithmetic average, which is the sum of all the observations divided by the number of observations.
MEAN(number)
For number, specify a column of numbers.
Column | Formula | Result |
---|---|---|
C1 contains 6, 3, 15 | MEAN(C1) | 8 |
Use the mean function to describe an entire set of observations with a single value that represents the center of the data. Many statistical analyses use the mean as a standard reference point.
The median function calculates the middle value of the data. Half the observations are less than or equal to the median. Half the observations are greater than or equal to the median.
If the data set contains an odd number of values, then the median is the middle value in the ordered data set. If the data set contains an even number of values, the median is the average of the two middle values. For example, for the set of numbers 1, 2, 3, 21, 35, 42, the median is the average of the two middle values (3 and 21), which is 12.
MEDIAN(number)
For number, specify a column of numbers.
Column | Formula | Result |
---|---|---|
C1 contains 6, 3, 15 | MEDIAN(C1) | 6 |
Use the median function to describe an entire set of observations with a single value that represents the center of the data.
Compared to the mean, the median is less sensitive to extreme data values. Thus, the median is often a more informative measure of the center of skewed data. For example, the mean may not be a good statistic for describing salaries within a company. The relatively high salaries of a few top earners inflate the overall average, giving a false idea of salaries at the company. In this case, the median is more informative. The median is equivalent to the 2^{nd} quartile or the 50^{th} percentile.
Function | Syntax |
---|---|
N missing for a column | NMISS(number) |
N nonmissing for a column | N(number) |
N total for a column | COUNT(number) |
For number, specify a column.
Column | Formula | Result |
---|---|---|
C1 contains *, 3, *, 7 | NMISS(C1) | 2 |
C1 contains *, 3, 4, *, 5 | N(C1) | 3 |
C1 contains 6, 3, *, 12 | COUNT(C1) | 4 |
The natural log (also called log base e) function calculates logarithms to the base e, where e is a constant that is equal to approximately 2.71828. The natural log of any positive number, n, is the exponent, x, to which e must be raised so that e^{x} = n. For example, e^{2} = 7.389, so the natural log of 7.389 is 2.
LN(number)
For number, specify a number or a column of numbers. Minitab calculates the value x such that e^{x} =number. If you enter 0 or a negative number, Minitab stores a missing value symbol *.
Formula | Result |
---|---|
LN(7.38905) | 2 |
You can use the natural log function in many ways, such as modeling exponential growth in biological populations and in financial theory, and calculating radioactive decay.
The natural log is also used in the calculation of probability density functions for many distributions.
The percentile function calculates percentiles for a sample. Percentiles divide the data set into parts. Usually, the n^{th} percentile has n% of the observations below it, and (100-n)% of observations above it.
For example, in the following graph, 25% of the total data values lie below the 25^{th} percentile (red region), while 75% lie above the 25^{th} percentile (white region).
PERCENTILE(number, probability)
Calculates the sample percentile, for a specified probability and number (the column containing the sample data). Missing values are ignored. The probability can be a number between 0 and 1, or a column of numbers between 0 and 1. For example, to determine the 1^{st} quartile (25^{th} percentile) for the data in column C1, enter C1 and 0.25.
Column | Formula | Result |
---|---|---|
C1 contains 2, 3, 5, and 7 | PERCENTILE (C1, 0.25) | 2.25 |
Minitab uses the empirical percentile function:
Term | Description |
---|---|
p | the percentage of data less than or equal to the desired percentile, divided by 100 |
X_{y} | the y^{th} row of the data when the data are sorted from least to greatest |
y | the truncated value of w |
w | p(N+1) |
N | the number of rows with nonmissing data |
z | w-y |
The permutation function calculates the number of permutations of n items chosen k at a time. A permutation is an ordered arrangement of objects from a group without repetitions. For example, there are six ways to order the letters abc without repeating a letter. The six permutations are abc, acb, bac, bca, cab, cba.
Permutations are used to calculate the probability of an event in an experiment with only two possible outcomes (binomial experiment).
PERMUTATIONS (number of items, number to choose)
Specify an integer or a column of integers for the number of items and the number to choose. The number of items must be greater than or equal to 1, and the number to choose must be greater than or equal to 0.
Suppose 10 people enter a contest. How many different ways can 1st, 2nd, and 3rd place be awarded when order is important?
Calculation expression | Result |
---|---|
PERMUTATIONS (10, 3) | 720 |
Permutations can also be used to determine the number of possible ways to order a group of letters or digits, which has applications in coding. Combinations and permutations, known as combinatorics, play an important role in network engineering, computer science (cryptography), molecular biology (pattern analysis), and other fields.
The range function calculates the difference between the maximum value and the minimum value.
RANGE(number)
For number, specify a column of numbers.
Column | Formula | Result |
---|---|---|
C1 contains 6, 3, 15 | RANGE(C1) | 12 |
The round function rounds a number based on the number of decimal places you specify.
ROUND(number, decimals)
For number, specify a number or a column of numbers that you want to round. For decimals, specify an integer.
Calculator expression | Result |
---|---|
ROUND(2.136, 0) | 2 |
ROUND(2.136, 1) | 2.1 |
ROUND(2.136, 2) | 2.14 |
ROUND(-2.136, 1) | -2.1 |
ROUND(253.6, -1) | 250 |
ROUND(253.6, -2) | 300 |
The square root function calculates, for any nonnegative number , the number n such that . The common notation for the square root of is or . The following is an example of the notation:
SQRT(number)
For number, specify a number or a column of numbers. If you enter a negative number, Minitab returns a missing value.
Formula | Result |
---|---|
SQRT(64) | 8 |
SQRT(0.25) | 0.5 |
The standard deviation function measures the dispersion of the data about the mean. Whereas the range estimates the spread of the data by subtracting the minimum value from the maximum value, the standard deviation approximately estimates the "average" distance of the individual observations from the mean. Larger standard deviation values indicate a greater spread in the data.
STDEV(number)
For number, specify a column of numbers.
Column | Formula | Result |
---|---|---|
C1 contains 6, 3, 15 | STDEV(C1) | 6.245 |
The sum function adds two or more numbers.
SUM(number)
For number, specify a column of numbers.
Column | Calculator expression | Result |
---|---|---|
C1 contains 6, 3, 15 | SUM(C1) | 24 |
The sum of squares function squares each value and calculates the sum of those squared values. That is, if the column contains x_{1}, x_{2}, ... , x_{n}, then sum of squares calculates (x_{1}^{2} + x_{2}^{2} + ... + x_{n}^{2}).
SUMSQ(number)
For number, specify a column of numbers.
Column | Formula | Result |
---|---|---|
C1 contains 6, 3, 15 | SUMSQ(C1) | 270 |