Download Weighted Means and Grouped Data on the Graphing

Weighted Means and Grouped Data on the Graphing Calculator
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
.
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.)
62 - 64
65- 67
68 - 70
71 - 73
74 - 76
Frequency (f)
3
7
9
8
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 the example above:
Height (in.)
62 - 64
65- 67
68 - 70
71 - 73
74 - 76
Height Class
Midpoint
(62 + 64)/2 = 63
(65 + 67)/2 = 66
69
72
75
Frequency (f)
∑
3
7
9
8
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.)