Data Analysis with Microsoft Excel: Updated for Office 2007

154 Fundamentals of Statistics

It’s particularly striking to note that the 90th percentile for home prices out-

side the northeast sector was $130,200, whereas for northeast sector homes

it was $172,650—$40,000 more. We noted earlier that there are more high-

priced homes in the northeast sector.

EXCEL TIPS

You can also get a table of cumulative percents using the Rank

and Percentile command in the Data Analysis ToolPak, an add-

in packaged with Excel.

You use the Data Analysis ToolPak to also create a table of

descriptive statistics.

Measures of the Center: Means, Medians, and the Mode

Another way to summarize a data set would be to calculate a statistic that

summarized the contents into a single value that we would think of as the

typical or most representative value. The table of percentiles suggests one

such value: the 50th percentile, or median. Because the median is located at

the 50th percentile, it represents the middle of the distribution: Half of the

values are less than the median, and half are greater than the median. Based

on the results from Figure 4-16, the median house price in the Albuquerque

sample from 1993 was $94,000 for nonnortheast sector homes, $98,000 for

northeast sector homes, and $96,000 overall.

The exact calculation of the median depends on the number of observa-

tions in the data set. If there is an odd number of values, the median is the

middle value, but if there is an even number of values, the median is equal

to the sum of the two central values divided by 2.

Another commonly used summary measure is the average. The average,

or mean, is equal to the sum of the values divided by the number of ob-

servations. This value is usually represented by the symbol x (pronounced

“x-bar”), a convention we’ll repeat throughout the course of this book.

Expressed as a formula, this is

x 5

Sum of values

Number of observations

5

x 11 x 21 c 1 xn

n

5

a

n

i 51

xi

n

•

•