Select the method or formula of your choice.

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 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 |

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

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

The smallest value in your data set.

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 largest value in your data set.

When the chosen statistic is a proportion, Minitab displays the proportion from the observed sample.
### Formula

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

x | number of events in the original sample |

N | number of trials in the original sample |

To analyze a proportion, Minitab does not take resamples from the original column of data. Instead, Minitab takes the resamples by randomly sampling from a binomial distribution. The number of trials and the event probability for the distribution are taken from the original sample.

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

c _{i} | chosen statistic of the i^{th} resample |

B | number of resamples |

N | number of observations in the original sample |

If the chosen statistic is a proportion, Minitab does not calculate a standard deviation.
### Formula

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

mean of the chosen statistic of the resamples | |

B | number of resamples |

c_{i} | chosen statistic of the i^{th} resample |

Sort the chosen statistic of the resamples in increasing order. *x*_{1} is the lowest number, *x*_{B} is the highest number.

Lower bound: *x _{l}* where =

Upper bound: *x _{u}* where =

To analyze a proportion, Minitab does not take resamples from the original column of data. Instead, Minitab takes the resamples by randomly sampling from a binomial distribution. The number of trials and the event probability for the distribution are taken from the original sample.

For a one-sided case (only a lower bound or upper bound), use α instead of α/2.

When *l* or *u* are not integers, Minitab does a linear interpolation between the two numbers on either side of *l* or *u*. The formula is:

*X _{y}* +

For example, if *l* = 5.25, the lower bound equals x_{5} + 0.25(x_{6} - x_{5}).

Minitab does not display the confidence interval when or .

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

α | 1- confidence level/100 |

B | number of resamples |

X _{y} | the y^{th} row of data when the data are sorted from least to greatest |

y | the truncated value of l or u |

z | l-y or u - y |