Think about those sled dogs from the Mode Concept one more time. We are going to analyze the data about speeds in a new way.
Alaskan sled dogs travel varying speeds during the Iditarod. These strong, wonderful animals can travel at an average speed of anywhere from 5 to 15 miles per hours.
Here are some speeds from the last Iditarod.
10 mph
12 mph
8 mph
15 mph
9 mph
8 mph
7 mph
12 mph
Now let's think about range. What is the range of the data?
This Concept will teach you how to figure out the range of a data set. We will come back to this problem at the end of the Concept.
Guidance
The range of a set of data is the difference between the greatest and least values.
To find the range of a set of data, subtract the largest data value from the smallest data value.
Let's look at how to apply this in a problem.
Determine the range for the set of data: 47, 56, 51, 45, and 41.
Subtract the largest data value, in this case 56 from the smallest data value of 41.
\begin{align*}56 - 41 = 15\end{align*}
The difference between the largest and smallest number is 15, therefore the range for this set of data is 15.
Now let's look at another one.
The chart below depicts the daily temperature in San Diego for the first seven days in August. Identify the range in temperatures.
Date: | Temperature: |
---|---|
Sunday 8/1 | \begin{align*}88^\circ F\end{align*} |
Monday 8/2 | \begin{align*}83^\circ F\end{align*} |
Tuesday 8/3 | \begin{align*}87^\circ F\end{align*} |
Wednesday 8/4 | \begin{align*}89^\circ F\end{align*} |
Thursday 8/5 | \begin{align*}82^\circ F\end{align*} |
Friday 8/6 | \begin{align*}79^\circ F\end{align*} |
Saturday 8/7 | \begin{align*}87^\circ F\end{align*} |
Subtract the largest value 89 from the smallest value 79.
\begin{align*}89 - 79 = 10\end{align*}
The range in temperatures is \begin{align*}10^\circ F\end{align*}.
Find the range of each data set.
Example A
\begin{align*}12, 14, 15, 16, 18, 20\end{align*}
Solution: \begin{align*}8\end{align*}
Example B
\begin{align*}14, 18, 19, 34, 32, 30, 41, 50\end{align*}
Solution: \begin{align*}36\end{align*}
Example C
\begin{align*}5, 10, 23, 20, 7, 9, 11, 18, 35, 16, 22\end{align*}
Solution: \begin{align*}30\end{align*}
Here is the original problem once again.
Alaskan sled dogs travel varying speeds during the Iditarod. These strong, wonderful animals can travel at an average speed of anywhere from 5 to 15 miles per hours.
Here are some speeds from the last Iditarod.
10 mph
12 mph
8 mph
15 mph
9 mph
8 mph
7 mph
12 mph
Now let's think about range. What is the range of the data?
To find the range, we must figure out the difference between the greatest and smallest values in the data set.
The greatest value is 15.
The smallest value is 8
Now we find the difference.
\begin{align*}15 - 8 = 7\end{align*}
The range of this data set is 7.
Vocabulary
- Data
- pieces of numerical information collected in a set.
- Mean
- the average value of a set of data.
- Median
- the middle value or score of set of data.
- Mode
- the value that appears the most in a set of data.
- Range
- the difference between the highest value and the lowest value of a set of data.
Guided Practice
Here is one for you to try on your own.
Think back to earlier Concepts about mean, median and mode. Now add what you have learned to range.
Should mean, median, mode, or range be determined to best analyze the following set of data?
Student: | Number of minutes: |
---|---|
1 | 29 |
2 | 32 |
3 | 40 |
4 | 33 |
5 | 38 |
Answer
Since there is not a number that occurs most often, the mode is not the best way to analyze the data.
Calculating the range of this data just allows one to see the difference between the students who finished the exam first and last.
In this case, determining the mean is the best way to analyze this data. The mean gives the average amount of time it took for the five students to complete the exam. In this case, the mean is 34.4 minutes. It can also be helpful to look at the median of this data, 33. In this case, the mean and median are close in value.
Remember to think about what the data describes and what your objective is in analyzing the data and this will help you to choose the best method for analyzing the data.
Video Review
This is a Khan Academy video on range.
Practice
Directions: Analyze each data set.
\begin{align*}32 \quad 29 \quad 40 \quad 35 \quad 42 \quad 25 \quad 40\end{align*}
1. Mean –
2. Median –
3. Mode –
4. Range –
The weekly paychecks for ten part-time employees are: $140, $132, $200, $150, $175, $200, $180, $95, $145, and $155.
5. Mean –
6. Median –
7. Mode –
8. Range –
The data set below depicts the number of points LeBron James scored in the last five NBA games.
\begin{align*}25 \quad 27 \quad 25 \quad 29 \quad 22\end{align*}
9. Mean –
10. Median –
11. Mode –
12. Range –
Here is the number of days that it took the mushers of the Iditarod to finish the race in 2010.
8 days, 9 days, 9 days, 9 days, 9 days, 9 days, 9 days, 9 days, 9 days, 9 days
13. Mean –
14. Median –
15. Mode –
16. Range –
A red lantern is the award given to the last musher to finish the Iditarod. The longest finish took place in 32 days. If the fastest time in 2010 was 8 days, what is the range between the last and the first?
17. Range –
The scores that Marc earned on his math quizzes were 78%, 85%, 88%, 88% and 90%
18. What is the mean of the data?
19. What is the mode of the data?
20. What is the median of the data?
21. What is the range of the data?
22. The table below depicts the amount of calories in various fast food choices. Which measure of the data will prove most reliable?
\begin{align*}& \text{Burger} && 375\\ & \text{Fries} && 210\\ & \text{Chicken Sandwich} && 300\\ & \text{Shake} && 215\\ & \text{Soda} && 159\end{align*}
23. Describe a situation where a mean would be the best way to analyze data.
24. Describe a situation where the range would be the best way to analyze data.