A commonly used measure of the center of a batch of numbers. The mean is also called the average. It is the sum of all observations divided by the number of (nonmissing) observations.
Term | Description |
---|---|
xi | ith observation |
N | number of nonmissing observations |
The standard error of the mean is calculated as the standard deviation divided by the square root of the sample size.
Term | Description |
---|---|
s | standard deviation of the sample |
N | number of nonmissing observations |
The sample standard deviation provides a measure of the spread of your data. It is equal to the square root of the sample variance.
Term | Description |
---|---|
x i | i th observation |
mean of the observations | |
N | number of nonmissing observations |
The variance measures how spread out the data are about their mean. The variance is equal to the standard deviation squared.
Term | Description |
---|---|
xi | ith observation |
mean of the observations | |
N | number of nonmissing observations |
The coefficient of variation is a measure of relative variability calculated as a percentage.
Minitab calculates it as:
Term | Description |
---|---|
s | standard deviation of the sample |
mean of the observations |
25% of your sample observations are less than or equal to the value of the 1st quartile. Therefore, the 1st quartile is also referred to as the 25th percentile.
Term | Description |
---|---|
y | truncated integer value of w |
w | |
z | fraction component of w that was truncated |
xj | jth observation in the list of sample data, ordered from smallest to largest |
When w is an integer, y = w, z = 0, and Q1 = xy.
The sample median is in the middle of the data: at least half the observations are less than or equal to it, and at least half are greater than or equal to it.
Suppose you have a column that contains N values. To calculate the median, first order your data values from smallest to largest. If N is odd, the sample median is the value in the middle. If N is even, the sample median is the average of the two middle values.
For example, when N = 5 and you have data x1, x2, x3, x4, and x5, the median = x3.
When N = 6 and you have ordered data x1, x2, x3, x4, x5,and x6:
where x3 and x4 are the third and fourth observations.
75% of your sample observations are less than or equal to the value of the third quartile. Therefore, the third quartile is also referred to as the 75th percentile.
Term | Description |
---|---|
y | truncated value of w |
w | |
z | fraction component of w that was truncated away |
xj | jth observation in the list of sample data, ordered from smallest to largest |
When w is an integer, y = w, z = 0, and Q3 = xy.
The interquartile range equals the third quartile minus the 1st quartile.
The mode is the data value that occurs most often in the dataset. If multiple modes exist, Minitab displays the smallest modes, up to a total of four. N for Mode is the number of times the mode (or modes) appears.
Minitab calculates the trimmed mean by removing the smallest 5% and the largest 5% of the values (rounded to the nearest integer), and then calculating the mean of the remaining values.
Term | Description |
---|---|
xi | i th observation |
The smallest value in your data set.
The largest value in your data set.
The range is calculated as the difference between the largest and smallest data value.
R = Maximum – Minimum
Minitab squares each value in the column, then computes the sum of those squared values.
Term | Description |
---|---|
xi | i th observation |
Skewness is a measure of asymmetry. A negative value indicates skewness to the left, and a positive value indicates skewness to the right. A zero value does not necessarily indicate symmetry.
Term | Description |
---|---|
xi | i th observation |
mean of the observations | |
N | number of nonmissing observations |
s | standard deviation of the sample |
Kurtosis is one measure of how different a distribution is from the normal distribution. A positive value usually indicates that the distribution has a sharper peak than the normal distribution. A negative value indicates that the distribution has a flatter peak than the normal distribution.
Term | Description |
---|---|
xi | i th observation |
mean of the observations | |
N | number of nonmissing observations |
s | standard deviation of the sample |
Minitab calculates half the MSSD (mean of the squared successive differences) of a batch of numbers. The successive differences are squared and summed. Then Minitab divides by 2 and calculates the average.
Term | Description |
---|---|
xi | i th observation |
mean of the observations |
The number of non-missing values in the sample.
The number of missing values in the sample. The number of missing values refers to cells that contain the missing value symbol *.
The total number of observations in the column.
Minitab calculates what percentage of the whole that is accounted for by each group.
Term | Description |
---|---|
ni | number of observations in the ith group |
N | number of nonmissing observations |
Minitab calculates the cumulative percentage that is represented by each group.
Term | Description |
---|---|
ni | number of observations in the ith group |
N | number of nonmissing observations |