Question

Suppose that six individuals are interested in taking part in a study relating BMI to a number of health outcomes. The following 6 numbers represent the individuals' BMI (kg/m2). a. 25.78 b. 21.06 c. 36.54 d. 29.51 e. 18.96 f. 34.05 A) What is the mean and median of the individuals' BMIs? B) Suppose that a BMI above 30 is considered obese. What is the relative frequency of obes in this group?

Answer 1

a) Mean = 27.65

Median = 27.645

b) Relative Frequency = 33.33%

Explanation:

We are given the following data set:

25.78, 21.06, 36.54, 29.51, 18.96, 34.05

a) Mean and Median

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`Mean =\displaystyle(165.9)/(6) = 27.65`

`Median:\\\text{If n is odd, then}\\\\Median = \displaystyle(n+1)/(2)th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle((n)/(2)th~term + ((n)/(2)+1)th~term)/(2)`

Sorted data: 18.96, 21.06, 25.78, 29.51, 34.05, 36.54

`\text{Median} = \displaystyle(25.78 +29.51)/(2) = 27.645`

b) BMI above 30 is considered obese

Frequency of obese in the given sample = 2

Relative Frequency =

`\displaystyle\frac{\text{Frequency of obese}}{\text{Total number}} = (2)/(6) = 0.3333 = 33.33\%`