QM 301 Chapter 3 (Sections 1 and 2)

Quartile

The 25th, 50th, and 75th percentiles, referred to as the first quartile, the second quartile (median), the third quartile, respectively. The quartiles can be used to divide a data set into four parts, with each part containing approximately 25% of the data.

Weighted Mean

The mean is obtained by assigning each observation a weight that reflects its importance. When the data are from a sample, this equation provides the weighted sample mean. If the data are from a population, μ replaces x̄ and the equation provides the weighted population mean.

Bimodal

When the data contains exactly two modes.

Multimodal

When the data contains more than two modes. In multimodal cases, the mode is almost never reported because listing three or more modes would not be particularly helpful in describing a location for the data.

Mean

A measure of central location computed by summing the data values and dividing by the number of observations. The mean is sometimes referred to as the arithmetic mean. If the data are for a sample, the mean is denoted by x̄; if the data are for a population, the mean is denoted by the Greek letter μ.

Median

A measure of central location provided by the value in the middle when the data are arranged in ascending order. With an odd number of observations, the median is the middle value. An even number of observations has no single middle value. Following conventions, we define the median as the average of the values for the middle two observations. Whenever a data set contains extreme values, the median is often the preferred measure of central location.

Geometric Mean

A measure of location that is calculated by finding the nth root of the product of n values.

Mode

A measure of location, that is the value that occurs with greatest frequency.

Coefficient of Variation

A measure of relative variability computed by dividing the standard deviation by the mean and multiplying by 100.

Standard Deviation

A measure of the variability computed by taking the positive square root of the variance.

Variance

A measure of variability based on the squared deviations of the data values about the mean. A measure of variability that utilizes all the data. The variance is based on the difference between the value of each observation and the mean.

Interquartile Range (IQR)

A measure of variability, defined to be the difference between the third and first quartiles.

Range

A measure of variability, defined to be the largest value minus the smallest value.

Population Parameters

A numerical value used as a summary measure for a population (ex. the population mean, μ, the population variance, σ^2, and the population standard deviation, σ). "If the measures are computed for data from a population, they are called population parameters."

Sample Statistic

A numerical value used as a summary measure for a sample (ex. the sample mean, x̄, the sample variance, s^2, and the sample standard deviation, s). "If the measures are computed for data from a sample, they are called sample statistics."

Point Estimator

A sample statistic, such as x̄, s^2, and s, used to estimate the corresponding population parameter. "In statistical inference, a sample statistic is referred to as the point estimator of the corresponding population parameter."

pth Percentile

For a data set containing n observations, the pth percentile divides the data into two parts: approximately p% of the observations are less than the pth percentile, and approximately (100-p)% of the observations are greater than the pth percentile. Denoted as Lp

Percentile

Provides information about how the data are spread over the interval from the smallest value to the largest value. A value such that at least p percent of the observations are less than or equal to this value and at least (100-p) percent of the observations are greater than or equal to this value. The 50th percentile is the median.

∑

Sigma, the summation sign.

Location of the pth Percentile

Lp = P/100(n+1) see page 111

Population Mean

The number of observations in a population is denoted by N and the symbol for a population mean is μ. **X to the i**