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Basic Statistics & Probability

Basic Statistics & Probability

At a Glance - Stem & Leaf Plots

Stem and Leaf Plots can be used to analyze data and display data all at the same time. This is a way of showing each data value along with its relationship to the other values.

If you turn a stem-and-leaf plot on its side, it's sort of like a histogram (more on this in the next topic).

To make a stem-and-leaf plot, create the "stem" by listing the largest place-value digits to the left of a vertical line. The remaining digits will be written to the right of the vertical line to create the "leaves". We know, that sounds pretty abstract. This plot is better explained using an example, so let's dive into one.

Here are the scores on last week's geometry test:

90, 94, 53, 68, 79, 84, 87, 72, 70, 69, 65, 89, 85, 83, 72

The largest place value that all the data have in common is the tens place. These digits will be our stems. We list these from least to greatest. Some people arrange them from greatest to least, but nerts to them.

stem leaf plot 1

Now we place the remaining digits of each data value in the leaf column. For example, to plot the value 84 we place a 4 to the right of the number 8. We also place all other data values in the 80s in that row.

stem leaf plot 2

Now rearrange the numbers so that each row is in numerical order (least to greatest).

stem leaf plot 3

The stem-and-leaf plot is a convenient way to look at the raw data. Using this plot we can see that most of the students scored in the 70's or 80's, and only one student earned a score less than 65.

Example 1

This stem and leaf plot represents the predicted high temperatures for New York City in the next 10 days.

stem leaf plot 4

5|7 represents a predicted temperature of 57 degrees Fahrenheit.

Use this plot to find the median of the data.

Example 2

This plot shows the top 20 final times for the two-man bobsled teams at the 2010 Winter Olympics.

stem leaf plot 6

3:26|65 represents a time of 3 minutes 26.65 seconds.

As you can see the difference between the gold medal winner and the bronze medal winner is less than 1 second (3:27.51 – 3:26.65 = 0.86 sec)!

Use this plot to find the mean time and the range for the top twenty bobsled teams.

Exercise 1

Create a stem and leaf plot for this data: 

50, 37, 48, 52, 51, 47, 38, 44, 39, 40, 41, 36, 32, 50, 44, 37, 45, 29.

Refer to this plot for exercises 2-4

This plot represents the amount of money Mateo earned the past 18 weeks working at his dad's shop. Use this stem and leaf plot to answer questions 2-4.

stem leaf plot 8

12|0 is $120

Exercise 2

 If Mateo saved half of each weekly paycheck, how much did he save?

Exercise 3

What was his mean paycheck?

Exercise 4

What was the median paycheck?

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