Question

Age at diagnosis for each of 20 patients under treatment for meningitis was given in a research paper. Suppose the ages (in years) were as follows.

18	18	27	19	23	20	66	18	21	18	20	18
18	20	18	19	28	16	18	18

(a)

Calculate the values of the sample mean and the standard deviation. (Round your standard deviation to three decimal places.)

sample mean =
rstandard deviation =

(b)

Compute the upper quartile, the lower quartile, and the interquartile range.

upper quartile=
lower quartile =
interquartile range =

(c)

Are there any mild or extreme outliers present in this data set? (Enter your answers as comma-separated lists. If there is no answer, enter NONE.)

mild outliers=

extreme outliers=

Answer 1

The Given Data of ages of patients is:

18	18	27	19	23	20	66	18	21	18	20	18
18	20	18	19	28	16	18	18

a) The sample mean is given by:

The sample standard deviation is given by:

b) Sorting the data:

16 18 18 18 18 18 18 18 18 18 19 19 20 20 20 21 23 27 28 66

First quartile is the observation of the data below which 25% of the observations falls.

Therefore Q1=(18+18)/2=18

Upper quartile is the observation above which 25% observations lies.

Q3=(21+23)/2=22

The interquartile range is IQR=Q3-Q1

           IQR=22-18=4

c) The points which are below Q1-1.5*IQR and above Q3+1.5*IQR are considered as a outliers.

Therefore Q1-1.5*IQR=18-1.5*4=18-6=12

and Q3+1.5*IQR=18+6=24

Therefore 27, 28 are mild outliers while observation 66 is extreme outlier.