Mark Krilanovich
©May 15, 2014
BUS 103
Chapter 22: Business Statistics
This chapter in a nutshell:
People in business often communicate numbers to each other. To save their time, this
chapter gives 5 ways to summarize a group of numbers.
Example:
Suppose you worked the following number of hours each day last week:
day:
hours:
Sun.
0
Mon.
2
Tues.
1
Wed.
4
Thurs.
3
Fri.
2
Sat.
5
•
Your boss asks you, "How much did you work last week?"
•
Your most accurate answer would be to tell him all 7 numbers; he would get bored.
•
This chapter shows 5 ways to briefly answer his question, to give him an
approximate feeling for how many hours you worked last week, to save his time.
•
Summarizing would be even more important with large groups of numbers, like how
many hours you worked last month.
The 5 ways to summarize (each with advantages) are:
1. The average (or mean) of the numbers.
2. The weighted mean of the numbers.
3. The median of the numbers.
4. The mode of the numbers.
5. The frequency distribution of the numbers.
The average or mean of a group of numbers
The mean of a group of numbers =
the sum of all the numbers in the group
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------the count of how many numbers are in the group
In the above example of hours worked last week:
0 hrs. + 2 hrs. + 1 hrs. + 4 hrs. + 3 hrs. + 2 hrs. + 5 hrs.
The mean hours per day = -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------7 days
17 hrs.
= --------------------------------------7 days
The mean hours per day = 2.43 hours/day
This is a summary way of saying how much you worked last week.
Chapter 22, page 2
The weighted mean of a group of numbers
The simplest example of this is your GPA or Grade Point Average; your grade in a
5-unit course affects your overall GPA more than your grade in a 2-unit course. This is
called weighted average because higher-unit courses "weigh more" in comparison to lowerunit courses.
Suppose your report card for last semester looks like this:
course:
Math
ACCT
Law
totals
units:
3
5
6
14
letter grade;
A
C
B
--
grade points:
4
2
3
--
12
10
18
40
units x grade points:
weighted average:
40
÷ 14 =
2.86
So if you interview for a job, and the interviewers asks you, "How were your grades
last semester?" it's quicker to answer, "My GPA was 2.86" than to list every grade in every
course. On the other hand, giving a single number loses some information; in my first term
in college, my GPA was a lousy 2.09, even though I got an A in my favorite subject.
Whenever I gave my GPA, I also mentioned that A. 
The median of a group of numbers
"Median" means "middle." The "median yellow line" on a road is down the middle.
The median of a group of number is the middle number, after sorted in order.
Let's go back to the number of hours you studied each day last week:
day:
hours:
Sun.
0
Mon.
2
Tues.
1
Wed.
4
Thurs.
3
Fri.
2
Sat.
5
4
3
2
5
Let's look just at the numbers of hours:
0
2
1
Now let's sort them from the smallest number to the largest number:
0
1
2
2
3
4
5
median
Because "2" is the middle of the 7 numbers, it is the median of the 7 numbers.
The "middle" of an odd number of values is easy to find, but what if we have an even
number of values? Then we have two "middle" numbers, and we simply average them:
1
2
The median is yet another
way to summarize a group of
of numbers. Each way has its
advantages and disadvantages.
©2010-2014 by Mark Krilanovich
4
5
6
median=
5+6
_____
2
=5.5
7
8
9
Chapter 22, page 3
The mode of a group of numbers
The mode of a group of numbers is the number that occurs most often in the group.
(Why? The word "mode" is a synonym for "mood," and maybe the number that occurs
most often is the "strongest" number, so it sets the "mood" for the group?)
In order to compute the mode of a group of numbers, it's easiest first to create a
frequency distribution table of those numbers, which is the next method we will study,
so this will save time in the next step.)
Over last Winter Break, I went wild, baking Christmas cookies (grandmother's recipes).
During the Twelve Days of Christmas, I baked these dozen cookies each day:
day:
1
2
3
4
5
6
7
8
9
10
11
12
dozen:
5
3
3
2
2
6
6
6
6
8
8
8
We want to compute the number of dozen cookies that I baked most often, so the
day numbers are irrelevant. Here are the dozen cookie counts:
5
3
3
2
2
6
6
6
Now let's sort the dozen counts from smallest to largest:
2
2
3
3
5
6
6
6
6
8
8
8
6
8
8
8
Now let's count ("tally") how many of each sized-batch I baked:
twice
count:
dozen:
2
three times
2
3
3
once
5
four times
6
6
6
three times
6
8
8
8
"6" occurs most often,
so it is the mode.
The frequency distribution of a group of numbers
The first 4 ways we've studied to summarize a group of numbers summarizes the
group into just one number: the mean, weighted mean, median, or mode. This is efficient
and compact, but to achieve that efficiency, it sacrifices additional information. The
frequency distribution is more efficient than telling someone all the numbers (especially if
that's hundreds or thousands of numbers), while also giving more information. It shows
how spread-out the numbers are, which none of the first 4 ways do.
To compute the frequency distribution, we first must count how many times each
number occurs, and create the last table shown above (was used for the mode).
Then we simply make a bar-graph of that data. The next pages shows "dozen cookies
baked" on the horizontal axis," and "number of days that sized-batch was made" on the
vertical axis (although either orientation would be correct).
©2010-2014 by Mark Krilanovich
Chapter 22, page 4
This shows more information than any of the first 4 summaries, because it shows how
many of each sized batch of cookies I baked, and how "spread out" the sizes were.
Correspondingly, it takes more room to show this more information. More importantly, it is
a visual presentation, and most people understand a picture immediately and intuitively,
whereas numbers might not be intuitive.
Summary
This chapter shows 5 ways to summarize a group of numbers. Each way has its own
advantages and disadvantages and are best suited for specific business needs.
Tips for the quiz:
1. Always show all your work.
2. Show what you will be trying to find (solve for).
3. Write down the formula to use.
4. Use the formula to find the answer.
5. Check: does your answer make sense?
6. Show all your work, to get credit.
©2010-2014 by Mark Krilanovich