Question

2.) Trade winds are one of the beautiful features of island life in Hawaii. The following data represent total air movement in miles per day over a weather station in Hawaii as determined by a continuous anemometer recorder. The period of observation is January 1 to February 15, 1971.

      26    113   27    72    16    32    17    35    18    21    11    15
      14    50    57    52    33    26    14    20    13    13    19    20
      18    13    28    105   18    11    57    21    18    25    22
      14    22    50    138   16    16    100   34    28    19    19

a.) Find the position of the median.

b.) Determine the median.

c.) Determine the quartiles.

d.) Write out the 5-number summary.

Test for outliers.
e.) Find the inner quartile range by subtracting the third quartile from the first quartile.

h.) Determine the lower and upper limits through the following equations.

ii.) Are there any outliers? If so which data value(s)?

j.) Above an appropriate x-scale, construct a modified boxplot.

Answer 1

a. The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

So here n=46 so Median position is average of 23rd and 24th value

b. Ordering the data from least to greatest, we get:

11   11   13   13   13   14   14   14   15   16   16   16   17   18   18   18   18   19   19   19   20   20   21   21   22   22   25   26   26   27   28   28   32   33   34   35   50   50   52   57   57   72   100   105   113   138   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median=

c. The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

11   11   13   13   13   14   14   14   15   16   16   16   17   18   18   18   18   19   19   19   20   20   21   21   22   22   25   26   26   27   28   28   32   33   34   35   50   50   52   57   57   72   100   105   113   138   

So, the bottom half is

11   11   13   13   13   14   14   14   15   16   16   16   17   18   18   18   18   19   19   19   20   20   21   

The median of these numbers is 16.

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

11   11   13   13   13   14   14   14   15   16   16   16   17   18   18   18   18   19   19   19   20   20   21   21   22   22   25   26   26   27   28   28   32   33   34   35   50   50   52   57   57   72   100   105   113   138   

So, the upper half is

21   22   22   25   26   26   27   28   28   32   33   34   35   50   50   52   57   57   72   100   105   113   138   

The median of these numbers is 34.

d. Five number summary

Is Minimum=11

Q1=16

Q2=21

Q3=34

Maximum-138