Unit 3. Information and the Internet
Revision Date: Jul 05, 2015 (Version 1.2)Summary: This lesson is designed for students to review basic statistics, including calculations of the mean, median, mode, and standard deviation. It will also give the students some experience using spreadsheet software to calculate the statistics and to create histograms. Note: This lesson is intended primarily as a review and a reminder of material that should already be familiar to the students. If your students have little familiarity or experience with using Excel to compute statistics or generate plots, you may wish to extend this lesson to two sessions, and provide more scaffolding and instruction on the basic mechanisms.
Outcomes:
Overview:
Source: This lesson was adapted from Unit 2: The Engineering Design Process, Lesson 2: Collecting and Processing Information ©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition/ Technology, Engineering, and Design
The students must understand the basic statistical concepts of mean, median, mode, and standard deviation. They must also be able to use spreadsheet software to calculate the statistics and to create histograms.
Students often have some initial difficulty learning how to use formulas in the spreadsheet software to do the calculations.
Student computer usage for this lesson is: required
For Each Student:
Review of Statistics:
Present a review of basic statistics (min, max, mean, median, mode, and range), and use the following board exercise to have the class review their understanding of these basic concepts:
Discussion:
Ask the class to come up with situations where it might be most useful to compute the mean, median, or mode of a set of values. Encourage them to understand that each of these statistics can be useful in different situations, but may be misleading. Have them generate sets of data that would give "misleading values" for mean (if there is an "outlier value"), median (if the values have a longer "tail" on one side than the other), or mode (if there is a frequent value that happens to occur at one end or the other of a wider range).
Note: The teacher may want to do this activity along with the students, displaying the spreadsheet on a screen so that the students may ask questions and see how to do the statistical calculations using the spreadsheet software. Students who do not have much experience with spreadsheets may need more scaffolding and instruction. (If you have many such students, you may wish to spread this lesson out over two class sessions.)
Students will use spreadsheet software, such as Excel, to calculate the average number and standard deviation of candy color in an individual-sized bag of M&Ms, Skittles, or other colored candy. Optionally, students may compare their results to other online published statistics for each candy.
Candy Statistics |
||||||
Trial Number |
1 |
2 |
3 |
4 |
5 |
6 |
Yellow |
17 |
20 |
24 |
19 |
19 |
17 |
Red |
21 |
13 |
19 |
21 |
15 |
18 |
Blue |
10 |
18 |
16 |
18 |
21 |
20 |
Brown |
7 |
12 |
5 |
12 |
12 |
14 |
Green |
26 |
26 |
16 |
17 |
22 |
18 |
Orange |
24 |
16 |
20 |
15 |
15 |
16 |
Package Total |
105 |
105 |
100 |
102 |
104 |
103 |
The students will also need to create columns further to the right labeled Mean, Median, Mode, and Standard Deviation.
Mean |
Median |
Mode |
Standard Deviation |
19.375 |
19 |
19 |
2.199837656 |
18.125 |
19 |
19 |
2.799872446 |
17 |
17.5 |
18 |
3.338091842 |
9.5 |
10 |
12 |
3.380617019 |
21.125 |
22 |
22 |
3.833592124 |
18.25 |
17.5 |
16 |
3.284161124 |
SUM
function.
Yellow Candy σ = |
2.199837656 |
Get on |
3Cs |
25.97451297 |
|
2S |
23.77467531 |
|
1s |
21.57483766 |
|
Mean |
19.375 |
|
-1s |
17.17516234 |
|
-2s |
14.97532469 |
|
-3s |
12.77548703 |
Students will answer the following question in their journals:
Learners may be paired to assist each other in the use of the spreadsheet software.
The teacher should frequently check the students' work for accuracy as the lesson progresses so that misunderstandings may be quickly resolved.