A pediatrician records the BMI for a number of his patients for a study he wishe
ID: 3300856 • Letter: A
Question
A pediatrician records the BMI for a number of his patients for a study he wishes to publish, and groups them into the following 4 categories: underweight, normal, overweight, and obese. The proportion of patients that fall into each category together with the middle weight of each category is also reported.
BMI Category
Class description and weight range
Underweight
(0-18.5)
Normal
(18.5-24.9)
Overweight
(25-29.9)
Obese
(30-35)
Class midpoint
9.25
21.7
27.45
32.5
Proportion (probability)
0.267
0.346
0.282
0.105
A) If we were to choose a patient from this pediatrician’s study at random, what BMI would you expect to receive? (Use the class midpoint for each BMI category and calculate the mean)
B) What is the variance of the distribution of patients in this pediatrician’s study?
C) Assume that the data are mound shaped and use the empirical rule to estimate the maximum weight in the obese category.
D) what(who) are the observational units in this study?
E) What are the measurements of interest?
F) Describe the population of interest.
G) Describe the sample in the study.
BMI Category
Class description and weight range
Underweight
(0-18.5)
Normal
(18.5-24.9)
Overweight
(25-29.9)
Obese
(30-35)
Class midpoint
9.25
21.7
27.45
32.5
Proportion (probability)
0.267
0.346
0.282
0.105
Explanation / Answer
(A) Expected value of BMI for a random patient = BMI midpoint * probability
= 9.25 * 0.267 + 21.7 * 0.346 + 27.45 * 0.282 + 32.5 * 0.105
x = 21.1314 BMI
(B) variance = (Midpoint - x )2 * probability
= (9.25 - 21.1314)2 * 0.267 + (21.7 - 21.1314)2 * 0.346 + (27.45 - 21.1314)2 * 0.282 + (32.5 - 21.1314)2 * 0.105
= 62.63
(C) Standard deviation = sqrt (variance) = 7.914 BMI
the data is mound shaped or say a normal distriubtion with mean BMI = 21.1314 and standard deviation = 7.914 BMi
The maximum weight is obese category will be mean + 3 * sigma = 21.1314 + 7.914 * 3 = 44.87BMI
(D) Observational UNits here are patients coming to the padetirician.
(E) measurement of interest here is BMI index of observation units.
(F) Population of interest here is people who are coming to check their BMI index.
(G) sample in the study is the person who gave her height and weight to calculate BMi for the study.
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