Question

The following is the data about number of tornadoes that touched down in the United States during each month of the year 1998.

47   72    182 102 373   120 82    60    104   86   25   6

1. What is the mean number of tornadoes that hit every month in 1998.
2. What is the median number of tornadoes that hit every month in 1998.
3. Which of the values would you consider to be outlier?
4. What are the mean and median if the outlier(s) is excluded?

e) Comment on the effect of extreme values on the mean and the median.

Answer 1

6 25 47 60 72 82 86 102 104 120 182 373

a) Mean = (6 + 25 + 47 + 60 + 72 + 82 + 86 + 102 + 104 + 120 + 182 + 373)/12 = 104.92

b) Median = (82 + 86)/2 = 84

c) Q1 = (47 + 60)/2 = 53.5

Q3 = (104 + 120)/2 = 112

IQR = Q3 - Q1 = 112 - 53.5 = 58.5

Q1 - 1.5 * IQR = 53.5 - 1.5 * 58.5 = -34.25

Q3 + 1.5 * IQR = 112 + 1.5 * 58.5 = 199.75

So the outlier is 373.

d) Mean = (6 + 25 + 47 + 60 + 72 + 82 + 86 + 102 + 104 + 120 + 182 )/11 = 80.55

Median = 82

e) Due to the extreme values, the mean and median values increases.