Select the method or formula of your choice.

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 |

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

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 |

The largest value in your data set.

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 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.

The smallest value in your data set.

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.

The number of non-missing values in the sample.

In this example, there are 141 recorded observations.

Total count | N | N* |
---|---|---|

149 | 141 |
8 |

The number of missing values in the sample. The number of missing values refers to cells that contain the missing value symbol *.

In this example, 8 errors occurred during data collection and are recorded as missing values.

Total count | N | N* |
---|---|---|

149 | 141 | 8 |

The total number of observations in the column. Use to represent the sum of N missing and N nonmissing.

In this example, there are 141 valid observations and 8 missing values. The total count is 149.

Total count | N | N* |
---|---|---|

149 |
141 | 8 |

The range is calculated as the difference between the largest and smallest data value.

R = Maximum – Minimum

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 |

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 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 |

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

x _{i} | i ^{th} observation |

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}.

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 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 |