Download Descriptive Statistics with the Graphing Calculator

Descriptive Statistics with the Graphing Calculator
Descriptive statistics include measures of center, such as the mean and median, and measures of spread
such as the standard deviation.
1. We will use the graphing calculator to obtain some descriptive statistics for heights of a sample of 30
males:
First, go to STAT 1:Edit, and enter the data into L1:
Now go to STAT CALC, and choose 1:1-Var Stats and then ENTER.
We see that the sample mean is
, the sample standard deviation is
and
the population standard deviation is
. Also, the sample size n = 30. (The sum of all
the heights is
, and the sum of the squares of the heights is
.) Use
the arrow key to scroll down:
We see that the minimum height is 62, the maximum height is 76, the Median is 69, the first
quartile is Q1 = 66, and the third quartile is Q3 = 72.
Note: If your data is contained in another list (besides L1), type the name of this list after 1-Var
Stats before you ENTER. For instance, if your data is in L2, you would type 2nd and the number
2 after 1-Var Stats:
2. Weighted Means. Suppose that, in a recent month, a bank customer had $2500 in his
account for 5 days, $1900 for 2 days, $1650 for 3 days, $1375 for 9 days, $1200 for 1 day, $900
for 6 days, and $675 for 4 days. To calculate the average balance for that month, you would
use a weighted mean:
To do this automatically on a calculator, enter the account balances in L1 and the number of
days (weight) in L2:
As before, go to STAT CALC and 1:1-Var Stats. This time, type L1, L2 after 1-Var Stats and
ENTER:
The weighted (sample) mean is
(so that the average balance for the month is
$1430.83.) We can also see that the weighted sample standard deviation is
.
3. Estimating the Mean and Standard Deviation from a Frequency Distribution. If your
data is organized into a frequency distribution, you can still estimate the mean and standard
deviation. For example, suppose that we are given only a frequency distribution of the heights
of the 30 males instead of the list of individual heights:
Height (in.)
Frequency (f)
62 - 64
3
65- 67
7
68 - 70
9
71 - 73
8
74 - 76
3
n = 30
We can just calculate the midpoint of each height class and use that midpoint to represent the
class. We then find the (weighted) mean and standard deviation for the distribution of midpoints
with the given frequencies as in Example 2 above:
Height (in.)
Height Class
Frequency (f)
Midpoint
62 - 64
(62 + 64)/2 = 63
3
65- 67
(65 + 67)/2 = 66
7
68 - 70
69
9
71 - 73
72
8
74 - 76
75
3
n = 30
The approximate sample mean of the distribution is
, and the approximate sample
standard deviation of the distribution is
. (These are only estimates of the true mean
and standard deviation of the sample because we are basing the calculations on the frequency
distribution, which is just a summary of the data, instead of the actual data.)