Question

Consider the following five-point summary that was obtained from the dataset of 200 observations.

Min Q1 Median Q3 Max

34 54 66 78 98

a. interpret Q1 and Q3

b Calculate the interquartile range . Determine whether any outliners exist.

c Is the distribution symmetric ? If not comment on its skewness

Answer 1

Part a

From given output for five point summary, the value of the first quartile or Q1 is given as 54, so we can say that about 25% of the observations in the data set are less than 54. The value of the third quartile or Q3 is given as 78, so you can say that about 75% of the values in the data set are less than 78.

Part b

Interquartile range is given as below:

IQ = Q3 – Q1

IQ = 78 - 54

IQ = 24

Interquartile range= 24

Inner Fence = Q1 – 1.5*IQ = 54 - 1.5*24 = 18

Outer Fence = Q3 + 1.5*IQ = 78 + 1.5*24 = 114

Min = 34 > 18

Max = 98 < 114

So, there is no any outlier present in the data.

Part c

Yes, distribution is symmetric because distances between two pairs (Q1, Q2) and (Q2,Q3) are same.

Q1 = 54

Q2 = 66

Q3 = 78

Q2 – Q1 = 12

Q3 – Q2 = 12