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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 |
---|---|

x_{i} | i^{th} 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.

If the column contains *x* _{1}, *x* _{2},..., *x* _{N}, with mean , then the standard deviation of the sample is:

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 |
---|---|

x_{i} | i^{th} 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 1^{st} quartile. Therefore, the 1^{st} quartile is also referred to as the 25^{th} percentile.

Term | Description |
---|---|

y | truncated integer value of w |

w | |

z | fraction component of w that was truncated |

x_{j} | j^{th} observation in the list of sample data, ordered from smallest to largest |

When w is an integer, y = w, z = 0, and Q1 = x_{y}.

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 x_{1}, x_{2}, x_{3}, x_{4}, and x_{5}, the median = x_{3}.

When N = 6 and you have ordered data x_{1}, x_{2}, x_{3}, x_{4}, x_{5},and x_{6}:

where x_{3} and x_{4} 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 75^{th} percentile.

Term | Description |
---|---|

y | truncated value of w |

w | |

z | fraction component of w that was truncated away |

x_{j} | j^{th} observation in the list of sample data, ordered from smallest to largest |

When w is an integer, y = w, z = 0, and Q3 = x_{y}.

The interquartile range equals the third quartile minus the 1^{st} 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 |
---|---|

x _{i} | 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 |
---|---|

x _{i} | 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 |
---|---|

x _{i} | 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 |
---|---|

x _{i} | 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 |
---|---|

x _{i} | 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 |
---|---|

n_{i} | number of observations in the i^{th} group |

N | number of nonmissing observations |

Minitab calculates the cumulative percentage that is represented by each group.

Term | Description |
---|---|

n_{i} | number of observations in the i^{th} group |

N | number of nonmissing observations |