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MGT 2250
Chapter 4
Graphically Summarizing Quantitative Data
Percentiles and Quartiles
The Interquartile Range (IQR)
Boxplot
The Five Number Summary
Range
Mean
Example
• Can 500 different songs fit on the iPod Shuffle?
▪ To answer this question, we must understand the typical length of a song and the variation of song
sizes around the typical length
▪ We can do this using summary statistics
▪ TABLE 1 Description of several digital recordings of songs.
▪
Song
Artist
Genre
Size (MB)
Length (sec)
My Friends
D. Williams
Alternative
3.83
247
Up the Road
E. Clapton
Rock
5.62
378
Jericho
k.d. lang
Folk
3.48
225
Dirty Blvd.
L. Reed
Rock
3.22
209
Nothingman
Pearl Jam
Rock
4.25
275
You can see that there is variation from reading the few rows of data in Table 1, but to understand
this variation, we need to consider all of the data.
We’ll first collapse all of the data on sizes into a few summary numbers. These summary numbers
that characterize a variable are known as summary statistics. We emphasize two types of summary
statistics that describe the typical value and variation of numerical data. One type of summary statistic
comes from putting the data in order, and the second type comes from averaging. We’ll then relate these
summary statistics to graphs that show a more complete view of a numerical variable.
Summary statistics
1. Median
The median is the 50th percentile, the value that falls in the middle when we sort the observations
of a numerical variable. Half of the observed values are smaller than the median, and half are larger.
If we have an even number of cases (n is even), the median is the average of the two values in the
middle. The units of the median match those of the data.
Definition: Median is a measure of central location provided by the value in the middle when the data are
arranged in ascending order.
2
First, Arrange the data in ascending order
a) for an odd number of observations, the median is the middle value
b) for an even number of observations, the median is the average of the two middle values
Example a): Use the example of 5 executives: 46, 54, 42, 46, and 32.
Arrange in ascending order: 32, 42, 46, 46, 54
n = 5 (odd), then:
Median = 46
Example b): Assume a new executive is added to the sample. 46, 54, 42, 46, 32, and 16.
Arrange in ascending order: 16, 32, 42, 46, 46, 54
n = 6 (even), then:
Median = (42+46)/2 = 44.
In Excel: Median =MEDIAN(RANGE)=44
Percentiles
The median is the 50th percentile, the value that falls in the middle when we sort the observations of a
numerical variable.
