HOW TALL ARE APRENDE 8TH

GRADERS?Algebra Statistics ProjectBy, 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

150 155 160 165 170 175 180 185 190

Height in Centimeters

BOX PLOT

150 155 160 165 170 175 180 185 190

Height in Centimeters

Lowest Number: 153 1st Quartile: 162Median: 1673rd Quartile: 173 Highest Number: 184

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

STANDARD DEVIATION

Height

153 -14.52 210.83

157 -10.52 110.67

158 -9.52 90.63

160 -7.52 56.55

160 -7.52 56.55

161 -6.52 42.51

163 -4.52 20.43

163 -4.52 20.43

164 -3.52 12.39

165 -2.52 6.35

165 -2.52 6.35

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

Height

171 3.48 12.11

171 3.48 12.11

172 4.48 20.07

174 6.48 41.99

175 7.48 55.95

175 7.48 55.95

177 9.48 89.87

178 10.48 109.83

184 16.48 271.59

Sum of the squared deviations

1,330.24

1,330.24 ÷ (25 – 1) = 55.43

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 tall 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