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

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