Stats: 3.1 Measure of center

Weighted mean

When different x data values are assigned different weights w, we can compute a weighted mean.

Multimodal mode

When more than two data values occur with the same greatest frequency, each is a mode and the data set is said to be multimodal

Bimodal mode

When two data values occur w/ the same greatest frequency, each one is a mode and the data set is said to be bimodal

Important properties of the median

-The median does not change by large amounts when we include just a few extreme values, so the median is a resistant measure of center -The median does not directly use every data value

Finding the mode

A data set can have one mode, more than one mode, or no mode.

Median

A data set is the measure of center that is the middle value wen the original data values are arranged in order of increasing (decreasing) magnitude.

the mean is not resistant

A disadvantage of the mean is that just one extreme value (outlier) can change the value of the mean substantially.

Mean

A set of data is the measure of center found by adding all of the data values and diving the total by the number of data values.

Measure of center

A value at the center or middle of a data set

Midrange not resistant

B/c the midrange uses only the max and min values, it is very sensitive to those extremes so the midrange is not resistant

Round off rules for measures of center

For the mean, median, and midrange, carry one more decimal than is present in the original set of values

Midrange

Midrange of a data set is the measure of center that is the value midway between the maximum values in the original data set. It is found by adding the maximum data value to the minimum data value and then dividing the sum by 2

Notion for the Median

The median of a sample is sometimes denoted by ~ x (pronounced "x-tidle) or M or Med

Mode

The mode of a data set is the value that occurs with the greatest frequency. It can be found w/ qualitative data.

Resistant

The presence of extreme values (outliers) does not cause it to change very much

Calculation for the Median

To find the median, first sort the values (arrange them in order) and then follow one of these procedures: 1.) If the number of data values is odd, the median is the number located in the exact middle of the sorted list 2.) If the number of data values is even, the median is found by computing the mean of the two middle numbers in the sorted list