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.
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 |