Module 2: Measures of Location – Ungrouped Data
The information in this module is contained in Chapter 3 in the text. This focus of this module is finding measures of
location in ungrouped data. Specifically, we’ll learn how to find and interpret the following:
1.
The Range (already covered in Module 1)
2.
Mode
3.
Mean
4.
Median
5.
Percentiles
6.
Quartiles
7.
The Interquartile Range
8.
The 5 Number Summary
We’ll first learn how to calculate these measures mathematically, then learn how to use Excel to find them. When
answering homework or test questions, you can use which ever method you want.

Module 2: Measures of Location – Ungrouped Data
1.
The Range (See Module 1)
2.
The Mode – The mode is the most frequently occurring value in a data set. It’s easiest to find by placing the data in ascending
order and looking for the most frequently occurring value. It’s possible for there to be no mode. It’s also possible for there to be
more than one mode:
If there are two modes, the data is bi-modal.
If there are three modes, the data is tri-modal.
If there are four or more, the data is multi-modal.
3.
The Mean – The Average
Let’s use the following data to find the mode and the mean.
First, we’ll put the data into ascending order (next slide)
150
149
145
144
89
116
139
128
112
118
143
116
156
175
122
167
139
120
110
171
118
134
178
102

Module 2: Measures of Location – Ungrouped Data
Mode – In looking at the ordered array, it’s clear this data set is tri-modal. There are two “116s”,
two”118s”, and two “139s”.
Had there, for example, been 3 “139s”, and everything else the same, 139
would have been the one and only mode.
Mean– The mean is calculated using the following formula:
is found by adding up all the numbers in the column.
This sums to 3241.
n is the sample size.
In this case, there are 24 values in the column
Therefore, the mean is
= 135.0417
Using Excel to calculate the mode and mean.
Mode:
Excel is not a good tool for finding the mode unless there is only one mode. If there is more than
one mode, Excel will only list one of them when using the mode command.
Mean:
Excel is an excellent tool for finding the mean.
89
102
110
112
116
116
118
118
120
122
128
134
139
139
143
144
145
149
150
156

Module 2: Measures of Location – Ungrouped Data
At the bottom of the column on the left, you’ll see the Excel formulas for calculating the mode and
median. Again note that Excel only lists the first mode in the ordered array, making Excel a poor tool
for finding the mode if there is more than one.
Note: The “(A1:A24)” part of the Excel command indicates the data is in the first 24 rows of
column A in Excel.
89
102
110
112
116
116
118
118
120
122
128
134
139
139
143
144
145
149
150
156

Module 2: Measures of Location – Ungrouped Data
4. The Median – The middle value of an ordered array of numbers (ascending order, although with a median it
technically could be descending order, too. But all other measures of location require ascending order). The
median divides the data into two equal parts. 50% of the data lies above the median, 50% lies below.

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- Spring '14
- DebraACasto
- Quartile