Download How tall are Aprende 8th Graders?

HOW TALL ARE
APRENDE 8 TH GRADERS?
Algebra Statistics Project
By, My Favorite Math Teacher
In my project I took the heights
of 25 Aprende 8th graders. I
was able to determine what the
average height is and was able
to see if there is a normal
distribution with the data.
GOOGLE FORM DATA
COLLECTION
QUESTIONNAIRE
GOOGLE SHEETS
RAW DATA
DOT PLOT
150
155
160
165
170
175
Height in Centimeters
180
185
190
BOX PLOT
150
155
160
165
170
175
180
185
190
Height in Centimeters
Lowest Number: 153
3rd Quartile: 173
1st Quartile: 162
Highest Number: 184
Median: 167
HISTOGRAM
NUMERICAL CALCULATIONS
IQR: 173-162 = 11cm
Mean:
153+157+158+160+160+161+163+163+164+165+
165+165+167+169+170+171+171+171+172+174+
175+175+177+178+184=4,188
4,188 ÷ 25 = 167.52 cm
Median: 167 cm
Height
(𝒙 − 𝒙)
𝒙− 𝒙
𝟐
Height
(𝒙 − 𝒙)
𝒙− 𝒙
153
-14.52
210.83
171
3.48
12.11
157
-10.52
110.67
171
3.48
12.11
158
-9.52
90.63
172
4.48
20.07
160
-7.52
56.55
174
6.48
41.99
160
-7.52
56.55
175
7.48
55.95
161
-6.52
42.51
175
7.48
55.95
163
-4.52
20.43
177
9.48
89.87
163
-4.52
20.43
178
10.48
109.83
164
-3.52
12.39
184
16.48
271.59
165
-2.52
6.35
165
-2.52
6.35
Sum of the squared
deviations
165
-2.52
6.35
167
-0.52
0.27
169
1.48
2.19
170
2.48
6.15
171
3.48
12.11
𝟐
1,330.24
1,330.24 ÷ (25 – 1) = 55.43
55.43 = 7.45
STANDARD
DEVIATION
The standard
deviation for
8th grade
height at
Aprende is
7.45 cm.
TWO-WAY FREQUENCY TABLE
150-159 160-169 170-179 180-189 Totals
Male
0
5
7
1
13
Female
3
6
3
0
12
Totals
3
11
10
1
25
150-159 160-169 170-179 180-189 Totals
Male
0%
20%
28%
4%
52%
Female
12%
24%
12%
0%
48%
Totals
12%
44%
40%
4%
100%
This data indicates
that males are taller
than females. 32% of
the males are 170 cm
or taller and only
12% of the females
are 170 cm or taller.
SUMMARY
Shape of data: The data displayed in the dot plot indicated that the data was
bimodal. This means it had two peaks in the data or two modes. The data in both
the box plot and the histogram were symmetric. This means that they data was
smaller on the left and right and gradually rose to a peak in the center. The data
was not skewed.
Standard deviation: The standard deviation for this project was 7.45 centimeters.
The mean was 167.52. If I add 7.45 to 167.52 and subtract 7.45 from 167.52, I
would find the heights of 68% of the 8th grade students in the project. This range is
160.07 to 174.97 cm. Ninety-five percent of the students in this project would be
within in two standard deviations of the mean. This range is 152.62 to 182.42 cm.
What I learned: I learned that the heights of the 8th grade Aprende students in my
project follow a normal distribution. This means that their heights follow a standard
pattern. The mean and median were almost identical (167.52 and 167). This
indicates that the data is symmetric. If someone were to ask me what the average
height of a random 8th grader is, I would have a 68% chance of getting it right if I
guessed somewhere in the range of 160 and 175 centimeters.
All images in presentation are from iclipart.com