The following lesson plans could be used for a three week unit adapted to the middle school or high school math class. The students will provide all the data for the statistical studies.
Lesson Plan I will introduce the student to surveys, recording data, and graphing bar graphs, histograms, and frequency curves.
Lesson Plan II is a study of the use of mean, median, and mode, using class attendance numbers.
Lesson Plan III is a correlation study between two variables. The variables are height and weight. The students can gather data from their own class and make a scatter diagram to see if they can find a correlation.
Lesson Plan IV is a further study of correlation of two variables. It consists of using the same heightweight data and scatter diagrams from Lesson Plan II, and checking it mathematically using the Pearson r.
Lesson Plan I: To Make Bar Graphs, Histograms, and Frequency Curves
Purpose To give the students practice in transposing data into a graph. Using data that the students compiled makes the graph more meaningful and fun for them.
Materials A survey form for each student. The questions may be either teacher designed or student designed. See sample survey below. Graph paper.
Procedure

1. Distribute the forms to the students. Tell the students they are NOT to sign their names.

2. Collect surveys.

3. Record data from filled out surveys by making tally marks for each question. (See example on following two pages.)

4. Post results on blackboard.

5. Count tally marks and change to frequency numbers on blackboard.

6. Give out graph paper.

7. Have students label x axis, Time, and y axis, Number of Students.

8. Do a sample graph from data on board on one of the results to a question in survey.

9. Have students make graphs from different assigned questions in survey.

____
NOTE: See following two pages for examples of graphing results of a survey question.

Example:
Sample Survey

1. What time do you usually go to sleep on a school night?

2. About how much time do you spend each school day:

3. What is your favorite:
T. V. show
Lesson Plan I
Examples: Sample Survey Question
(figure available in print form)
Lesson Plan I
Examples: Sample Survey Question
What is your favorite ice cream flavor?
The answers to this question in the survey can only be graphed as bar graph because the horizontal x axis will not have quantity numbers (cardinal numbers), but only names of ice cream flavors. The answers to
What time do you usually go to sleep on a school night?
, that were graphed on the preceding page have quantity numbers (time and number of students on the x and y axis), so the survey answers to that question can be either a frequency curve, histogram, or bar graph.
What is your favorite ice cream flavor?
(Hypothetical Data)
20 Students
(figure available in print form)
Lesson Plan II:
Study of Mean, Median, Mode, Using Student Attendance
Numbers
.
Purpose To study the meaning of central tendencies like mean, median mode using numbers that relate to the students, like their own class attendance record for two weeks.
Procedure

1. Post the attendance record for two weeks on board for a class of 20 students.

Example:

1st Week

2nd Week


M

T

W

TH

F

M

T

W

TH

F


18

19

15

14

19

18

17

18

20

15


2. To find the
mean
(X), add all the numbers and divide by the number of days. 173 = 17.3 = 17. So 17 is the mean, or the average number of students present in class per day.

3. To find the
median
, arrange the numbers in descending order. 20, 19, 19, 18, 18, 18, 17, 15, 15, 14, and take the middle number. Since 10 is an even number, take the 5th and 6th number and average them. The 5th and 6th numbers are 18, 18, so the median = 18.

4. To find the mode, take the number that has the greatest frequency, that is, 18 because it occurs three times, while 19 and 15 only occur two times. So the mode = 18.
Lesson Plan III: To do a correlation study using scatter diagrams
.
Purpose To show students that there is an easy way to see if there is a correlation between two variables such as height and weight by making a scatter diagram.
Procedur:

1. Distribute paper to students, and ask then to write their height and weight, but not their name.

2. Collect papers.

3. Write the heights on the board in ascending order, together with the corresponding weights.

4. Have the students make a graph putting weight on the X axis and height on the Y axis.

5. Graph each point (height, weight) as though each pair of numbers were (X, Y) of an ordered pair. Example: (5’4, 115)

6. Draw a straight line through the pattern of points to see if there is a linear relation.

Example:

Height

Weight

Height

Weight


5’2”

105 lbs.

5’9”

148 lbs.


5’4”

115 “

5’10”

156 “”


5’5”

132 “

5’11”

171 ‘’


5’7”

145 “

5’11”

177 “”


5’9”

160 “

6’1”

185 ‘’

(figure available in print form)
Lesson Plan IV: Pearson r Formula
Purpose To check the correlation of height and weight found from the scatter diagram in Lesson Plan III, with a mathematical formula called the Pearson r. This will be good calculator practice for the students. It will also be a review of order of operations when the students fit the data into the Pearson r formula.
Method

1. Use the heights and weights from Lesson Plan III.

2. Change the heights from Lesson Plan III into inches (for example: 5’2” = (5x12) + 2 = 62 inches).

3. Put the weight in the first column (x).

4. Put the height in inches in third column (y).

5. Square each weight for column 2 (x
^{
2
}
).

6. Square each height for column 4 (y
^{
2
}
).

7. Multiply the weight times the height for column 5 (xy).

8. Add each of the columns and put total at bottom beside.
(figure available in print form)
9.
(figure available in print form)

10. Fit numbers into formula from table above, noting the order of operations, that is multiply and divide, before you subtract.
(figure available in print form)
Hint for remembering order of operations.
P
lease,
M
y
D
ear
A
unt
S
ally. The first letter of these words helps the student remember the order of operations which is
P
arenthesis,
M
ultiply,
D
ivide,
A
dd,
S
ubtract.
Conclusions Since a 1 or 1 shows perfect correlation, the result of 0.98 shows almost perfect correlation. If r = 0, then there is no pattern in a scatter diagram or zero correlation between the two variables being studied. This hypothetical data gave an unusually high correlation. A negative correlation shows a line sloping negatively and signifies an inverse type of relationship, such as the faster he runs, the less time it will take him to get to a fixed destination.
positively sloping line

negatively sloping line

(figure available in print form)
Definitions

array—arrangement of data according to magnitude, from smallest to largest.

bar graph—a form of graph that employs bars to indicate the frequency of observations within each category.

cumulative percentile—the percentages of cases at or below a given point.

cardinal number—a number that represents quantity like height, weight, time, money, numbers, that can be used in all mathematical operations.

data—numbers or measurements that are collected as a result of observations.

frequency data—how many times an event occurs in each class of a given variable. Example: How many babies between 6 and 7 lbs, were there among the group of 118 babies.

frequency curve a form of graph representing a frequency distribution in which a continuous line is used to indicate the frequency (f) of corresponding scores.

interval scale—quantitative scale that permits the use of arithmetic operations. The zero point is arbitrary.

histogram—a form of bar graph used with interval of ratio scaled frequency distributions.

measure of central tendency—index of central position employed in the description of a frequency distribution. Uses mean, median, mode, and deviations from mean.

mean—the average; called X. Adding up the weight of 8 people and dividing by 8 to get the mean or average weight. X = X

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N

median—the score of the middle person when scores are arranged sequentially. If there are an even number of subjects, the average of the two middle subjects.

mode—the score or measurement that the greatest number of subjects share.

ordinal numbers—numbers that represent rank or position in a series. Example: 1 = always is a good listener, 2 = usually is a good listener, 3 = sometimes is a good listener, 4 = never is a good listener.

ratio scale—same as interval scale except has a zero point.

dispersion—how spread out the curve is on each side of the mean.

random sample—a method of selecting samples so each sample of a given size shares an equal chance of being selected.

range—the crude range is the scale distance between the largest and the smallest score.

standard deviation—a measure of how spread out a curve is on either side of the mean. SS = sum of the squared deviations from the mean.
(figure available in print form)