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Basic Statistics & Probability

Basic Statistics & Probability

At a Glance - Histograms

Histograms are another convenient way to display data. A histogram looks similar to a bar graph, but instead of plotting each individual data value on the x-axis (the horizontal one), a range of values is graphed. Histograms are useful when you have numerical data that varies quite a bit.

This is a histogram of the top 20 men's 2-man combined bobsled times for the 2010 Winter Olympics. Only the seconds are graphed, since each time began with 3 minutes.

2010 olympics

The times are marked on the x-axis, and the frequency (the number of teams who got each time) is graphed on the y-axis (the vertical one). By looking at the graph we can see that seven teams had a final time between 3:30 and 3:31 (3 minutes 31 seconds) and no teams had a time between 3:31 and 3:32.

This histogram has a "bin width" of 1 sec, meaning that the data is graphed in groups of 1 sec times. We could change the bin width to be larger or smaller. Here is the same data in a histogram with a bin width of 1.5 seconds:

The histogram doesn't display the individual times, nor are the times exact. However it is a nice way to look at the trend of the data.

Example 1

Create a histogram displaying the top ten women's figure skating scores for the 2010 Winter Olympics

Figure Skating
Yu-Na Kim228.56
Mao Asada205.5
Joanie Rochette202.64
Mirai Nagasu190.15
Miki Ando188.86
Laura Lepisto187.97
Rahail Flatt182.49
Akiko Suzuki181.44
Alena Leonova172.46
Ksenia Makarova171.91

The x-axis needs to span from at least 171 to 229 in order to accommodate all of the data.

Example 2

This histogram represents the scores from the last geometry test. They are graphed with a bin width of 7.

geometry scores

a) How many students took the test?

Use the graphs below to answer questions #1-4

These histograms graph the amount of time (hours per day) that 46 middle school girls and 40 middle school boys in San Francisco spend on the website FaceSpace. 50 boys and 50 girls took the survey but 4 girls and 10 boys did not use these sites at all. Each is graphed with a bin width of 0.25 hours.

social networking (girls)

social networking (boys)

Exercise 1

How many boys spend more than 1.5 hours/day on social networking sites?

Exercise 2

Compare the percentage of boys and girls that spend more than zero but less than 1 hour/day on these sites.

Exercise 3

Find the interval where the median of the boys' data set lies

Exercise 4

What can you conclude based on these graphs?

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