Title: Temperature Analysis (Measures of Central Tendency) Mathematics Content: Mean, Median, Mode, Range & Discussing and analyzing these measures of central tendency Objectives: To calculate and explore various means, medians, modes and ranges for quantitative data. To record use these quantities to make predictions, analyze and discuss data. Time: Approximately one 50 minute class period MN Standards: Grade 7; Strand‐ Data Analysis and Probability; Benchmark‐ 7.4.1.1 “Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions. “ Materials: Activity worksheet (one per student), thermometers (at least one per group) and probes, ice water for each student to drink, a piece of gum for each student Instructors’ Notes: Students need to be in groups of 3‐5. Students should not be chewing gum, eating candy, etc. at the beginning of this activity. Each student should have their own activity worksheet, so that they will be able to calculate their own mean temperatures as well as work with the group. There are also follow‐up questions at the end of this activity, which students could work on individually for homework. The “follow‐up questions” may also be used to engage students in a group discussion. The water must be ice water or very cold water for the activity to work. Enrichment: Follow‐Up Questions (Can be done in groups or individually), Extra Homework Practice TEMPERATURE ANALYSIS Name:________________________ Group Members’ Names:_________ _____________________________ Hour:_________________________ SHOW ALL WORK FOR EACH STEP 1. It is often quoted that the average temperature of the human body is 98.6° F. Will 98.6° always be the average? Also, is 98.6° the median? Would it be the mode? Will there be a big range of data? Before beginning this experiment, take a few moments to record your thoughts and predictions. Use the table below to record your data throughout the experiment. Round to the nearest tenth. ORIGINAL TEMPERATURE NAME TEMPERATURE AFTER WATER TEMPERATURE AFTER GUM 2. Each group member needs to take their temperature twice. Use the Fahrenheit measure and wait at least thirty seconds between readings. Record your temperatures and your group temperatures in the table above. Round to the nearest tenth of degree throughout this experiment. a. What is the average of just your original temperatures?______________ b. Concerning all (both of yours and all of the groups) original temperatures, 1. What is the average temperature? ________________________ 2. What is the median temperature? ________________________ 3. What is the mode temperature? _________________________ 4. What is the range of the temperatures? ___________________ 3. Drink approximately ten swallows of water. Again, take two temperature readings, waiting at least 30 seconds between each reading. Record your group’s data in the table. (Begin chewing a piece of gum while answering the following questions. This will get you ready for question #4.) a. What is the average of just your temperatures after drinking water?_____________ b. Concerning all (both of yours and all of the groups) temperatures taken after drinking water, 1. What is the average temperature? _______________________ 2. What is the median temperature? ________________________ 3. What is the mode temperature? _________________________ 4. What is the range of the temperatures? ___________________ 4. After chewing a piece of gum for a few minutes (which you should have begun in question #3), take two temperature readings, again waiting at least 30 second between each reading. Record your group’s data in the table. a. What is the average of just your temperatures after chewing gum?_____________ b. Concerning all (both of yours and all of the groups) temperatures taken after chewing gum, 1. What is the average temperature? _______________________ 2. What is the median temperature? ________________________ 3. What is the mode temperature? _________________________ 4. What is the range of the temperatures? ___________________ 5. Using ALL of the temperatures recorded in your chart, a. Calculate the mode temperature ________________________________ b. Calculate the range of the temperatures___________________________ c. Calculate the median temperature________________________________ d. Calculate the mean temperature. Can it be calculated more than one way? If so, show as many different ways to calculate the mean as possible. And, explain why it can be calculated more than one way. 6. Revisit the questions in #1. Were your predictions correct? Were most of your temperature readings and your groups’ temperature readings close to 98.6°? Did 98.6° prove to be the average? Explain your thoughts. Follow‐up questions 1. If doctors are trying to get a patient’s fever down, would giving the patient gum be helpful? How about water? Explain your thoughts. 2. Why would it be useful for a doctor to know an ill patients’ mean temperature? Mode? Range? Median? Which do you think would be the most important for the doctor to know? Why? 3. Alien Stovey from Saturn has an average body temperature of 519.4° F and he joined your group. He took two “original temperatures” and those were added to your chart. Concerning all of the original temperatures (question #2,) would the mean change very much? Would the median? Would the mean or the median be a more accurate representation of the data? Explain all of your answers. 4. How would a person know if the mean or the median is a more accurate representation of a certain set of data? 5. In the earlier activity, why was it important to wait a few seconds between each temperature reading? 6. Besides drinking water or chewing gum, what might be some other things a person could do to try to alter their body temperature? 7. What would be another real‐life situation where finding the mean would be useful? Create your own story problem based on this situation. Include the data set, and solve the problem. Be creative! Pre –Test
The number of skittles in a fun size package is as follows: 19, 24, 20, 20, 21, 18, 23, 20
1. What was the skittles most common amount? What do we call this amount? Why would it be useful to
know this?
2. What was the median of the amount of skittles?
3. What do you realize about the answers in #1 & #2?
4. Will the median and the mode always be the same answer? Explain.
5. What was the highest amount of skittles?
6. What was the lowest amount of skittles?
7. What is the difference between the highest and lowest amounts? What do we call this? Why would this be
useful for a company to know?
8. What is the average amount of skittles? What is another word for “average?” Why would this be useful for
a company to know?
Post –Test
The number of skittles in a fun size package is as follows: 19, 24, 20, 20, 21, 18, 23, 20
1. What was the skittles most common amount? What do we call this amount? Why would it be useful to
know this?
2. What was the median of the amount of skittles?
3. What do you realize about the answers in #1 & #2?
4. Will the median and the mode always be the same answer? Explain.
5. What was the highest amount of skittles?
6. What was the lowest amount of skittles?
7. What is the difference between the highest and lowest amounts? What do we call this? Why would this be
useful for a company to know?
8. What is the average amount of skittles? What is another word for “average?” Why would this be useful for
a company to know?
Mean, Median, Mode, Range, Outlier
Extra Practice Worksheet
Name:__________________
Period:________________
Date:___________________
Define the following.
Mean:
Median:
Mode:
Range:
Outlier:
Arrange the numbers in ascending order, then find the median, mode, range, and outlier(s). Show all of
your work!
1.
15, 22, 19, 7, 4, 7, 5, 13, 22
2.
3, 5, 7, 4, 2, 6, 8, 1, 9, 34
Order:___________________
Order:____________________
Mean:___________________
Mean:____________________
Median:__________________
Median:__________________
Mode:____________________
Mode:____________________
Range:___________________
Range:___________________
Outlier:___________________
Outlier:___________________
A class’s test scores were as follows: 100, 84, 92, 92, 90, 96, 89, 88, 92
3. What was the class’s most common test score? What do we call this score? Why would it be useful for the
teacher to know this?
4. What was the median test score?
5. What do you realize about the answers in #4 & #5?
6. Will the median and the mode always be the same answer? Explain.
7. What was the class’s highest score?
8. What was the class’s lowest score?
9. What is the difference between the highest and lowest scores? What do we call this? Why would this be
useful for a teacher to know?
10. What is the average test score? What is another word for “average?” Why would this be useful for a teacher
to know?
11. If the classes scores listed above were percentages, did the class do well? Explain your answer.
12. Is there an outlier in the grades above? Explain.