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In Fall 2016, more than 1500 Stat 100 and Stat 200 students responded to an anomymous survey at the beginning of the semester. Two questions asked in the survey were their height and weight. The computer randomly selects 200 students from the data set. The following shows the weights (in pounds) and heights (in inches) from the random sample.
weight <- c(137, 191, 130, 175, 112, 200, 125, 185, 120, 105, 250, 125, 204, 113, 160, 215, 163, 137, 132, 93, 140, 145, 90, 90, 125, 148, 120, 130, 140, 160, 127, 130, 140, 175, 143, 138, 170, 109, 120, 140, 105, 243, 120, 126, 282, 155, 107, 132, 133, 138, 120, 140, 120, 150, 110, 90, 128, 150, 130, 185, 175, 127, 250, 149, 161, 180, 218, 175, 85, 88, 140, 135, 126, 112, 240, 170, 150, 142, 105, 136, 140, 140, 120, 160, 190, 165, 135, 115, 130, 167, 107, 175, 160, 139, 113, 135, 180, 100, 111, 200, 145, 112, 150, 130, 97, 150, 153, 96, 145, 140, 149, 117, 125, 135, 205, 110, 219, 140, 145, 152, 80, 140, 120, 186, 240, 150, 140, 160, 102, 133, 124, 160, 108, 200, 137, 145, 145, 170, 145, 245, 100, 80, 105, 126, 114, 106, 150, 160, 198, 140, 145, 145, 137, 252, 195, 142, 135, 157, 95, 135, 145, 150, 150, 140, 300, 150, 135, 190, 132, 200, 180, 155, 182, 176, 135, 135, 135, 175, 165, 107, 156, 145, 110, 143, 150, 160, 125, 120, 120, 200, 195, 134, 165, 170, 139, 172, 150, 110, 100, 101)
height <- c(68, 75, 62, 71, 62, 72, 64, 67, 63, 63, 78, 65, 64, 64, 69, 76, 70, 70, 72, 61, 69, 62, 64, 65, 60, 69, 68, 62, 67, 73, 65, 62, 72, 71, 63, 67, 69, 60, 64, 63, 63, 72, 60, 67, 71, 70, 60, 72, 65, 64, 65, 65, 64, 67, 65, 60, 68, 66, 63, 71, 70, 63, 72, 67, 70, 70, 73, 72, 62, 68, 70, 70, 62, 65, 63, 69, 72, 63, 65, 60, 65, 66, 67, 74, 72, 70, 63, 62, 67, 65, 62, 75, 67, 69, 62, 71, 63, 58, 65, 67, 71, 67, 77, 63, 63, 63, 64, 63, 65, 61, 63, 63, 67, 66, 73, 67, 66, 68, 68, 68, 76, 68, 63, 67, 68, 66, 70, 64, 62, 66, 62, 68, 62, 70, 66, 67, 72, 62, 65, 64, 60, 58, 61, 64, 64, 60, 63, 68, 68, 67, 70, 70, 62, 73, 74, 68, 63, 73, 64, 68, 67, 70, 72, 68, 75, 70, 66, 70, 66, 71, 70, 71, 70, 67, 64, 64, 63, 71, 69, 61, 63, 64, 63, 60, 64, 66, 63, 66, 65, 82, 71, 67, 70, 61, 56, 67, 67, 62, 65, 65)
Copy and paste the commands to your R and execute them.
The body mass index (BMI) is defined as the body mass divided by the square of body height. The BMI is an attempt to quantify the amount of tissue mass (muscle, fat, and bone) in an individual, and then categorize that person as underweight, normal weight, overweight, or obese based on that value.
BMI is usually measured in units of kg/m2, resulting from mass in kilograms and height in metres. In our survey data, weight is measured in pounds and height is measured in inches. So we need to do a conversion. One pound of weight corresponds to a mass of 0.4536 kg and one inch is 0.0254 m, simple calculation shows that
BMI (in kg/m2) = 703 × (Wpound / H2in) ,
where Wpound is the body weight in pounds and Hin is height in inches.
Use the formula to calculate the BMI of the students in the sample. Be sure to use the conversion factor 703 in your calculation; otherwise your answers may not agree with computer's answers.
a. What are the mean and sample standard deviation of the BMI in the sample? Give your answers to 2 decimal places.
Mean = kg/m2
sample standard deviation = kg/m2
b. What is the median of the BMI in the sample? Give your answer to 2 decimal places.
Median = kg/m2
c. Calculate the correlation matrix between weight, height and BMI. Give your answers to 3 decimal places.
Correlation between weight and height =
Correlation between weight and BMI =
Correlation between height and BMI =
d. What are the maximum and minimum of BMI in the data? Give your answers to 2 decimal places.
Maximum BMI = kg/m2, minimum BMI = kg/m2.
e. What are the weight and height corresponding to the maximum BMI? If there are ties in the maximum BMI, find the weight and height of the first occurrence of maximum.
Consistency check: make sure the weight and height give you the maximum BMI you calculated in (d).
Weight = pounds, height = inches.
Is this student the heaviest in the sample? yes no
Is this student the shortest in the sample? yes no
f. What are the weight and height corresponding to the minimum BMI? If there are ties in the minimum BMI, find the weight and height of the first occurrence of minimum.
Consistency check: make sure the weight and height give you the minimum BMI you calculated in (d).
Is this student the lightest in the sample? yes no
Is this student the tallest in the sample? yes no
