3.23: Stem-and-Leaf Plots, Mean, Median and Mode
Do you remember calculating the mean, median and mode of a data set? You can also use a stem - and - leaf plot to find these measures. Here is Julie's stem - and - leaf plot once again.
This Concept will show you how to use Julie's stem - and - leaf plot to find the mean, median and mode of the data set.
Guidance
Remember back to when you learned about data?
We worked with data sets and found the mean, median and mode of each set of data.
The mean is the average of a set of data.
The median is the middle number of a set of data.
The mode is the number that occurs the most in a set of data.
We can use a stem-and-leaf plot to find the mean, median and mode of a set of data.
Here we have a data set with numbers that range from 35 to 59. The largest interval is from 55 to 59. The smallest interval is from 35 to 38.
What is the mean for this set of data?
To find the mean, we add up all of the numbers in the set and divide by the number of values that we added.
35 + 36 + 37 + 38 + 40 + 40 + 41 + 42 + 43 + 55 + 55 + 55 + 56 + 57 + 58 + 59 = 747
We divide by the number of values, which is 16.
\begin{align*}\frac{747}{16} = 46.68\end{align*}
After rounding, our answer is 47.
What is the median for this set of data?
Well, remember that the median is the middle score. We just wrote all of the scores in order from the smallest to the greatest. We can find the middle score by counting to the middle two scores.
42 + 43 These are the two middle scores.
We can find the mean of these two scores and that will give us the median.
42 + 43 = 42.5
The median score is 42.5 for this data set.
What is the mode for this data set?
The mode is the value that appears the most.
In this set of data, 55 is the number that appears the most.
The mode is 55 for this data set.
Use this stem - and - leaf plot to answer the following questions.
Example A
What is the mean?
Solution: 30
Example B
What is the median?
Solution: 28.5 or round up to 29
Example C
What is the mode?
Solution: There isn't a mode for this data set.
Now back to Julie.
Here is Julie's stem - and - leaf plot once again.
What is the mean?
What is the median?
What is the mode?
To find the mean we add up all of the values in the data set and divide by the number of values in the set.
\begin{align*}52 + 67 + 70 + 75 + 78 + 78 + 86 = 506\end{align*}
\begin{align*}506 \div 7 = 72.2\end{align*}
The mean is 72.
To find the median, we look for the middle score.
The median value is 75.
To find the mode, we look for the value that appears the most.
The mode of this set is 78.
Vocabulary
Here are the vocabulary words in this Concept.
- Stem-and-leaf plot
- a way of organizing numbers in a data set from least to greatest using place value to organize.
- Data
- information that has been collected to represent real life information
- Mean
- the average of a data set.
- Median
- the middle value in a data set.
- Mode
- the value that occurs the most in a data set.
Guided Practice
Here is one for you to try on your own.
What is the mean, median and mode of this data set?
Stem | Leaf |
---|---|
2 | 9 |
3 | 1 |
4 | 0 5 |
5 | 2 |
6 | 2 |
7 | 6 |
8 | 3 |
9 | 2 2 |
Answer
To find the mean, we add up the weights and divide by the total number of weights.
\begin{align*}29 + 31 + 40 + 45 + 52 + 62 + 76 + 83 + 92 + 92 = 602\end{align*}
\begin{align*}602 \div 10 = 60.2\end{align*}
The mean is 60.
To find the median, we look for the middle value of the data set.
The median is between 52 and 62. So we find the average of those two numbers.
\begin{align*}52 + 62 = 114 \div 2 = 57\end{align*}
The median value is 57.
To find the mode, we look for the value that appears the most.
The mode of the data set is 92.
Video Review
Here are videos for review.
Khan Academy Stem-and-Leaf Plots
Great video on organizing, building and interpreting a stem and leaf plot.
http://www.mathplayground.com/howto_stemleaf.html
Practice
Directions: Answer each question.
1. Define the mean.
2. Define the median.
3. Define the mode.
Directions: Use the stem and leaf plot to answer the following questions.
Stem | Leaf |
---|---|
6 | 8 |
7 | 5 7 9 |
8 | 0 2 |
9 | 2 6 6 7 |
4. What is the lowest value in the plot?
5. What is the greatest value in the plot?
6. Which interval has the most values in it?
7. What is the mean of the data set?
8. What is the median of the data set?
9. What is the mode of the data set?
10. What is the range of the data set?
Stem | Leaf |
---|---|
0 | 8 |
1 | 2 7 8 9 |
2 | 2 3 |
3 | 1 5 |
4 | 0 |
11. What is the smallest value in the plot?
12. What is the greatest value in the plot?
13. What is the mean of the data set?
14. What is the median of the data set?
15. What is the mode of the data set?
Data
Data is information that has been collected to represent real life situations, usually in number form.Mean
The mean of a data set is the average of the data set. The mean is found by calculating the sum of the values in the data set and then dividing by the number of values in the data set.Median
The median of a data set is the middle value of an organized data set.Mode
The mode of a data set is the value or values with greatest frequency in the data set.Stem-and-leaf plot
A stem-and-leaf plot is a way of organizing data values from least to greatest using place value. Usually, the last digit of each data value becomes the "leaf" and the other digits become the "stem".Image Attributions
Here you'll learn to use a stem - and - leaf plot to find the mean, median and mode.
Concept Nodes:
Data
Data is information that has been collected to represent real life situations, usually in number form.Mean
The mean of a data set is the average of the data set. The mean is found by calculating the sum of the values in the data set and then dividing by the number of values in the data set.Median
The median of a data set is the middle value of an organized data set.Mode
The mode of a data set is the value or values with greatest frequency in the data set.Stem-and-leaf plot
A stem-and-leaf plot is a way of organizing data values from least to greatest using place value. Usually, the last digit of each data value becomes the "leaf" and the other digits become the "stem".