Transcript Central Tendency

# credit card returns: (on the calculator…)
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Quantitative Graphs
Central Tendency
Center

Roughly describes where the center of the
data is in the set.

Can use the mean or the median
Mean
Sample:
Population:
x

x
n
x


N
The following show the # of hours spent by college professors
in teaching and advising. Find the average # of hours they spend
teaching & advising.
Show your Work –
including the formula
that you used!
The 50 states plus the District of Columbia have a total of 3137
counties. There are a total of 248,709,873 people in each of
these counties. Find the average population per county.
248,709,873

3137
  79,282.7 residents/county
What if I used the Almanac Book of Facts and chose a few
samples?
Sample 1
Sample 2
Sample 3
20,095
28,895
16,934
108,978
10,032
519
15,384
16,174
73,478
13,931
959,275
14, 798
24,960
30,797
13,859
x  209,034.6
x  23,917.6
x  36,669.6
We’ll study this further to see how to be
able to use samples to predict the
populations better.
Median

This is the value in the middle

50% of the data is above and below this
value.
Find the Median – first put the values in
order (smallest to largest)
6, 8, 12, 14, 17
Median = 12
7, 15, 22, 23, 27, 28
22  23
median 
2
median  22.5
Find the mean & median of the following
tests grades.
20
97
93
84
71
85
87
94
88
76
92
88
98
89
60
x 1222



 81.5
N
15
Stemplot:
median  84
The mean is greatly affected by outliers –
it’s very sensitive to them – which means it
is pulled towards the outlier.
The median is insensitive to outliers. It’s
often used more because it is more stable.
Examples

Average salaries of professional football
players.

Scores on a test when there’s one that hasn’t
been made up yet.

Average salaries of 1st year teachers
mean
median
mod e
mode median mean
mean median mod e
Proportion of Success:
M
F
F
M
F
M
F
F
M
F
Proportion of Females
For a Population use π.
F
F
8
p
14
# successes
p
n
M
M
Trimmed Mean
Order the data – delete a selected number of
values from each end of the list then average
the remaining values.
Trimming Percentage: It’s the percent of
values trimmed from the list.
Dive Scores
6
5
2
8
5
7
5
7
6
7
Let’s do a 10% trim.
Ed took 5 tests and his average was 85. If his average
after the first three tests was 83, what’s the average of
the last two tests.
On Thursday, 20 out of 25 students took a test and their average
was 80. On Friday, the other 5 students took it and their average
was 90. What was the class average?
The first 3 hours of a trip, Susan drove 50 mph. Due to delays,
she drove 40 mph for the next 2 hours. What was her average
speed?
Ed’s average on 4 tests is 80. What does he need to get on the
5th test to raise his average to an 84?