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Histograms
Histogram: Class width
Range = Largest – Smallest
Rangewidth =
#classes
28 32 44 21
45 38 40 22
mpg of cars: 27 21 23 25 25
25 23 22 24 27
29 28 22 38 18
26 33 27 52 43
But…you can also just pick any scale as long as it is consistent.
mpg of cars: 27 21 23 25 25
25 23 22 24 27
29 28 22 38 18
26 33 27 52 43
Salaries of CEO’s (nearest thousand):
250 621 262
750 368 659
862 204 206
149 350 242
145 396 572
Using the calculator
Put data in L1 Go to 2nd y= Turn on, turn on histogram (make sure xlist is
L1 or whatever list your data is in) Hit zoom9 Go to window. Set xmin to smallest value
and scl = class width. Press graph. (Trace will show all values)
# credit card returns:
36 57 75 73
32 49 63 35
35 35 47 39
28 42 41 24
Cautions…
Don’t confuse Histograms with Bar Graphs
Don’t use count (in a frequency table) or percents (in a relative frequency table) as data.
When comparing distributions with different numbers of observations you must use percentages instead of counts!
Central Tendency
Center
Roughly describes where the center of the data is in the set.
Can use the mean or the median
Mean
xx
n
x
N
Sample:
Population:
The following show the # of hours spent by college professors in teaching and advising. Find the average # of hours they spend teaching & advising.
423
13
32.5
xx
n
x
x
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
313779,282.7 residents/county
The following data represents the travel times to work of a sample of 15 North Carolina residents. Find the mean.
0 5
1 000025
2 005
3 00
4 00
5
6 0
Key: 2|5 is a NC worker who travels 25 minutes to work.
Do you think this represents the data well?
What if I used the Almanac Book of Facts and chose a few samples?
Sample 1
20,095
108,978
15,384
13,931
24,960
Sample 2
28,895
10,032
16,174
959,275
30,797
Sample 3
16,934
519
73,478
14, 798
13,859
36,669.6x 209,034.6x 23,917.6x
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
7, 15, 22, 23, 27, 28
Median = 12
22 23
222.5
median
median
The following data represents the travel times to work of a sample of 15 North Carolina residents. Find the median.
0 5
1 000025
2 005
3 00
4 00
5
6 0
Key: 2|5 is a NC worker who travels 25 minutes to work.
Do you think this represents the data well?
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
mod
mean
median
e
mode median mean
modmean median e
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?
Homework
Page 45 (53, 55, 56, 59, 65, 79, 81, 83, 85)