The sample size (N) is the total number of observations in the original sample. Minitab takes resamples of this sample size to form the bootstrap samples.
The mean is the average of the data, which is the sum of all the observations divided by the number of observations.
For example, the wait times (in minutes) of five customers in a bank are: 3, 2, 4, 1, and 2. The mean waiting time is calculated as follows:
On average, a customer waits 2.4 minutes for service at the bank.
The mean is an estimate of the population mean. Because the mean is based on sample data and not on the entire population, it is unlikely that the sample mean equals the population mean. To better estimate the population mean, use the confidence interval.
StDev (observed sample)
The standard deviation is the most common measure of dispersion, or how spread out the data are about the mean. The symbol σ (sigma) is often used to represent the standard deviation of a population, while s is used to represent the standard deviation of a sample. Variation that is random or natural to a process is often referred to as noise. Because the standard deviation is in the same units as the data, it is usually easier to interpret than the variance.
The standard deviation of the observed sample is an estimate of the standard deviation of the population.
Use the standard deviation to determine how spread out the data are from the mean. A higher standard deviation value indicates greater spread in the data. A good rule of thumb for a normal distribution is that approximately 68% of the values fall within one standard deviation of the mean, 95% of the values fall within two standard deviations, and 99.7% of the values fall within three standard deviations. The standard deviation of the sample data is an estimate of the population standard deviation.
The standard deviation can also be used to establish a benchmark for estimating the overall variation of a process.
The variance measures how spread out the data are about their mean. The variance is equal to the standard deviation squared.
The greater the variance, the greater the spread in the data.
Because variance (σ2) is a squared quantity, its units are also squared, which may make the variance difficult to use in practice. The standard deviation can be easier to use because it is a more intuitive measurement. For example, a sample of waiting times at a bus stop may have a mean of 15 minutes and a variance of 9 minutes 2. Because the variance is not in the same units as the data, the variance is often displayed with its square root, the standard deviation. A variance of 9 minutes2 is equivalent to a standard deviation of 3 minutes.
The sum is the total of all the data values. The sum is also used in statistical calculations, such as the mean and standard deviation.
The minimum is the smallest data value.
In these data, the minimum is 7.
Use the minimum to identify a possible outlier or a data-entry error. One of the simplest ways to assess the spread of your data is to compare the minimum and maximum. If the minimum value is very low, even when you consider the center, the spread, and the shape of the data, investigate the cause of the extreme value.
The median is the midpoint of the data set. This midpoint value is the point at which half the observations are above the value and half the observations are below the value. The median is determined by ranking the observations and finding the observation that are at the number [N + 1] / 2 in the ranked order. If the number of observations are even, then the median is the average value of the observations that are ranked at numbers N / 2 and [N / 2] + 1.
The median and the mean both measure central tendency. But unusual values, called outliers, affect the median less than they affect the mean. When you have unusual values, you can compare the mean and the median to decide which is the better measure to use. If your data are symmetric, the mean and median are similar.
The maximum is the largest data value.
In these data, the maximum is 19.
Use the maximum to identify a possible outlier or a data-entry error. One of the simplest ways to assess the spread of your data is to compare the minimum and maximum. If the maximum value is very high, even when you consider the center, the spread, and the shape of the data, investigate the cause of the extreme value.