3.1 Measure of Center

Properties of the mode

1) A data set may not have a mode 2)A data set may have one or more than one mode 3) If a mode exists for a data set, the mode is a value in the data set 4) Not affected by outliers in the data set 5) Only measure of center appropriate for qualitative data

Properties of the median

1) Easy to compute by hand 2) Only determined by middle values of a data set, not affected by outliers 3) May not be a value in the data set if there are even number values in the set 4) Useful measure of center for skewed distributions

Determining the most appropriate measure of center

1) For Qualitative data, the mode should be used 2) For Quantitative data, the mean should be used, unless the data set contains outliers or is skewed 3) For Quantitative data sets that are skewed or contain outliers, the median should be used

Finding the median of a data set

1) List the data in ascending (or descending order), making an ordered array 2) If the data set contains an ODD number of values, the median is the middle value in the ordered array. 3) If the data set contains and EVEN number of values, the median is the arithmetic mean of the two middle values in the ordered array.

Graphs and measures of center

1) The mode is the data value at which a distribution has its highest peak 2) The median is the number that divides the area of the distribution in half 3) The mean of a distribution will be pulled toward any outliers

Properties of the mean

1) most familiar and widely used measure of center 2) Its value is affected by every value in the data set 3) May not be a value in the data set 4) Appropriate measure of center for quantitative data with no outliers

No mode

Describes a data set in which all of the data values occur only once or each value occurs an equal number of times

Bimodal

Describes a data set in which exactly two data values occur equally often

Multimodal

Describes a data set in which more than two data values occur equally often

Unimodal

Describes a data set in which only one data value occurs most often

Population mean

The arithmetic mean if all values in a population

Sample Mean

The arithmetic mean of a set of sample data

Weight mean

The mean of a data set in which each data value in the set does not hold the same relative importance

Median

The middle value in the ordered array of data

Arithmetic mean

The sum of all the data values derived by the number of data values, often simple called the mean

Mode

The value in a data set that occurs most frequently