Question

The following are body mass index scores measured in 12 patients who are free of diabetes and participating in a study of risk factors for obesity. body mass index is measured as the ratio of weight in kilograms to height in meters squared. Using the following data, compute the mean BMI, the standard deviation of BMI, the median BMI and the Q1 and Q3. Are there outliers in the distribution of BMI? Justify your answer.

25 27 31 33 26 28 38 41 24 32 35 40

Answer 1

Answer: a) Mean BMI = xbar = sum(BMI)/12 = 31.67

b) Standard Deviation BMI = sqrt((sum(BMIi - xbar)²)/11) = 5.88

c) Median = average of 6th and 7th observation = 31.5

d) Q1 = 1st quartile = value below which 25% of the data lies. So, Q1 = 26.75

e) Q3 = 3rd quartile = value below which 75% of the data lies. So, Q3 = 35.75

Outliers can be detected by 1.5*IQR rule, which states that any point in the dataset below Q1 - (1.5*IQR) and above Q3 + (1.5*IQR) is an outlier.

Here Q1 - (1.5*IQR) = 13.25 and Q3 + (1.5*IQR) = 49.25.

Since no datapoint in the dataset is less than 13.25 or greater than 49.25, we can say that there are no outliers in the distribution of BMI.