Download Lab 3

Math 101 – Lab 3 – Standard Deviation
Consider the following data about the number of sales per week at two different dealerships:
Weekly sales
4
5
6
7
8
9
10
Number of occurrences (frequency)
Dealership A
Dealership B
2
15
3
0
9
1
20
12
14
15
3
48
1
13
Problem 1. Enter the data for Dealership A and Dealership B into Excel (create 2 different tables,
Dealership A first and then Dealership B below it).
Next to the frequency for each dealership, use Excel to find the relative frequency (add this to you
table):
1
2
3
4
5
A
Dealership A
Weekly Sales
4
5
…
B
C
Frequency
2
3
…
Rel. Freq
??
??
…
Create a table using Excel of the relative frequencies for each dealership.
Problem 2. For each dealership, find the mean number of weekly sales. Be careful, you have to
take a weighted mean (just like for the GPA calculations). For example, for Dealership A, 4 sales in
one week happens twice, 5 sales in one week happens 3 times, etc.
If you were buying a car dealership based on which one sells more cars per week on average,
which one would you pick?
Computing the standard deviation.
Recall that the distribution of a data set describes the values taken on and their frequencies. To
describe the distribution we have statistical variables such as range (max value – min), mean
(average), median (middle point of values), and mode. It is also possible to discuss how the
distribution is skewed (left or right or not at all).
Variation describes how spread out the data is from the center. One way to measure and display
variation is with the 5-number summary and the accompanying box plot. The five numbers in the
5-number summary split the collection of values into quarters.
Another way to describe variation is with the standard deviation. It’s a measure of how far your
data points are from the mean. The larger the standard deviation, the more spread out.
Standard deviation =
sum of (data value  mean) 2
number data values 1
How do you compute this?

1.
2.
3.
4.
5.
Find the mean of your data set.
For each data point, take (data point – mean)2.
Add this up for every data point.
Divide by the number of data points -1.
Take the square root of this.
Problem 3. For the following data points, find the mean and compute the standard deviation:
1, 2, 3, 6, 7, 9
Do the same for the following data:
2, 3, 4, 4, 5, 5
Which distribution is more spread out?
Note: there is a built in function in Excel that will do this for you – stdev()
Problem 4.
In a new tab in Excel, create an entry for each weekly sales count (there should be 52).
It should look something like this:
1
2
3
4
5
6
7
8
9
A
Weekly Sales
4
4
5
5
5
Etc.
B
C
 two 4’s
 three 5’s
Now with this list of data points, find the standard deviation just as in Problem 3. You can use
Excel to do the calculation in steps.
For example:
1
2
3
4
5
6
7
8
A
Weekly Sales
4
4
5
5
5
Etc.
B
Data value mean
=(A2 – mean)
C
Squared
D
E
Take the square
root of the sum
over (52 – 1)
 this is the
standard
deviation
=B2^2
Sum up the
squared terms
9
Dealership B has 104 entries. Is there an easier way?
Problem 5. Now using Excel, find the standard deviation for the weekly sales data for each
dealership.
Be careful, just like with the mean, for Dealership A there are 2 data points for 4 sales, 3 for 5 sales,
etc.
You can use the following table to do this calculation:
1
A
B
Dealership A
2
Weekly
Sales
3
4
4
5
5
6
7
8
9
10
6
7
8
9
10
11
Freq
2
3
9
20
14
3
1
C
D
Sales x
Freq.
Data value
– mean
=A3*B3
=A3 – C12
E
F
Previous
column
squared
=(D3)^2
Multiply by
number of
data points
=E3 * B3
G
 
Total
number
of weeks
Sum (sales
x freq)
Sum up
above
Mean
=C10/B10
Standard
Deviation
12
13
=sqrt(F11/(B11-1)
Which dealership shows greater variation in their number of weekly sales? Which dealership is
more consistent in their sales?
Does it agree with what you would conclude about consistency based on the graphs you created in
Problem 1?
Save your Excel file and email it to me at the end of class.
My email is [email protected]
Also hand in this worksheet at the end of class. If you do not finish, please
complete on your own and hand in by Wednesday, October 19th.