QBA 260 Chapter 4

Measures of Central Tendency Statisticians use measures of central tendency as a way of describing dataStatisticians use measures of central tendency as a way of describing data Three common measures of central tendency are:Three common measures of central tendency are: Mean (Average)Mean (Average) Median – the middle value in the datasetMedian – the middle value in the dataset Mode – the value that occurs most frequently in the datasetMode – the value that occurs most frequently in the dataset

Calculating an Average  The data are represented by x 1, x 2, x 3,…, x n x 1, x 2, x 3,…, x n  The average is the sum of the data values divided by the number of data values

Calculating an Average  Data: 12, 14, 9, 12, 8 Sum: = 55 Sum: = 55 n: 5 n: 5

Excel Functions  AVERAGE Uses only numbers Uses only numbers  AVERAGEA Treats text as zeroes unless the text is TRUE Treats text as zeroes unless the text is TRUE  TRIMMEAN Eliminates the most extreme values before calculating the average Eliminates the most extreme values before calculating the average

Trimmed Average  Deletes the most extreme lower and upper values  40% trimmed 1, 2, 3, 4, 5 1, 2, 3, 4, 5 1, 2, 30, 4, 5 1, 2, 30, 4, 5 1, 2, 300, 4, 5 1, 2, 300, 4, 5

The Median  The median is the value in the middle when the data are ordered  10, 12, 15, 18, 21, 34, 88  10, 12, 15, 18, 21, 34

The Mode  The mode is the most common value  1, 2, 3, 2, 4, 6, 2, 3, 1, 5, 4

Scales of Measurement  Average Interval or ratio data Interval or ratio data  Median Ordinal, interval or ratio data Ordinal, interval or ratio data  Mode Nominal, ordinal, interval, or ratio data Nominal, ordinal, interval, or ratio data