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Measures of Spread
Section 1: The Range
The high temperatures for April in the Charlotte Area for 5 consecutive years are listed below. Use this
information to answer the questions
Highest Temperature in Degrees Fahrenheit: 77, 86, 84, 93, 90
1. What is the range of high temperatures in April?
2. Are the numbers close together or far apart?
3. How does the range support your answer in number 2?
Section 2: The Interquartile Range
Using the same data from section 1, answer the questions below:
1. What is the Median of the high temperatures in April?
2. The First Quartile is the Median of the data less than the Median.
a. What is all of the data less than the Median?
b. What is the Median of this data?
c. What is the First Quartile?
2. The Third Quartile is the Median of the data more than the Median.
a. What is all the data greater than the Median?
b. What is the Median of this Data?
c. What is the Third Quartile?
3. The Interquartile Range is another way to describe how spread out a data set is. We find the
Interquartile Range by finding the difference between the Third Quartile or Q3 and the First Quartile Q1.
What is the interquartile range for the high temperatures?
4. Does the interquartile range support your conclusion on how far apart the data is? Explain.
5. Why do you think the Interquartile Range is less than the Range?
Section 3: The Standard Deviation
Standard Deviation is another way to measure spread. Standard Deviation is based on distance from the
mean instead of distance between two numbers.
Here is how you calculate the Standard Deviation
1. Find the distance between each data point and the mean. This is called the Deviation from the Mean
2. Square each distance. This is called the Squared Deviation.
3. Find the Mean of the Squared Deviations and take the square root
4. Once you take the square root, you have found the Standard Deviation
1. What is the mean of the high temperatures of April?
2. Complete the Table below to find the Deviation from the Mean and the Squared Deviation for each
data point
Data Value
77
86
84
93
90
Deviation from Mean
77-86=-9
Squared Deviation
−92 = 81
3. Find the Mean of the Squared Deviations:
4. Take the Square Root of the Mean of the Squared Deviations:
5. Standard Deviation=
6. Your answer to 5 is considered One Standard Deviation from the Mean. Figure out How many
Standard Deviations away from the Mean Each Data Point is
Data Value
77
86
84
93
90
Number of Standard Deviations
About 1
None
About 1
About 1
About 1
7. Is your conclusion about how far apart the data set is supported by the Standard Deviation? Explain.
Section 4: Application
NFL Player’s Average Ages
Team
Bears
Bengals
Broncos
Chiefs
Colts
Eagles
Jets
Lions
Packers
Patriots
Saints
Seahawks
Steelers
Texans
Titans
Average Age
25.8
26
26.3
25.7
25.1
25.2
26.1
26.4
25.9
26.6
26.3
26.2
26.8
25.6
25.7
1. What do you notice about the Average Age of NFL Players?
2. Find the Range of the Data. Does this support your conclusion from number 1? Explain.
3. Using your Calculator, you are going to find the First Quartile, Third Quartile, the Interquartile Range,
and the Standard Deviation
1. Press Stat and enter
2. Put the Average Age in L1
3. Press Stat and go over to Calc
4. Press 1.
5. The following symbols are important to know
Mean:𝑥̅ (𝑐𝑎𝑙𝑙𝑒𝑑 𝑋 𝐵𝑎𝑟), Median: MED (Will need to scrolls down), Q1: First Quartile, Q3: Third Quartile,
and Standard Deviation: σx
6. Fill in each piece of information using your calculator
Mean:
Median:
Standard Deviation:
First Quartile:
Third Quartile:
Interquartile Range:
7. What does the Standard Deviation tell you about the spread of the data?
8. What does the Interquartile Range tell you about the spread of the data?
9. Do our measures of spread (Standard Deviation, Range, and Interquartile Range) support what you
concluded about the data? Explain.
10. Using the following data find the Standard Deviation, Range, and Interquartile Range. Then make a
conclusion about the spread of the data
MLB Player’s Average Age
Team
Astros
Cardinals
Cubs
Diamondbacks
Dodgers
Giants
Marlins
Mets
Nationals
Padres
Pirates
Phillies
Reds
Rockies
Yankees
Mean:
Standard Deviation:
Interquartile Range:
Conclusion:
Average Age
28.5
29.0
28
27.8
29.5
29.1
26.9
28.9
28.6
28.7
26.9
30.5
28.7
28.9
29.3
11. What is the typical age of a NFL Player?
12. What is the typical age of a MBL Player?
13. Which one has more variation (spread): NFL or MBL and what would account for that spread?