2.) Trade winds are one of the
2.) Trade winds are one of the beautiful features of island lifein Hawaii. The following data represent total air movement in milesper day over a weather station in Hawaii as determined by acontinuous anemometer recorder. The period of observation isJanuary 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 quartilefrom the first quartile.
h.) Determine the lower and upper limits through the followingequations.
ii.) Are there any outliers? If so which data value(s)?
j.) Above an appropriate x-scale, construct a modifiedboxplot.
Answer:
a. The median is the middle number in a sorted list ofnumbers. So, to find the median, we need to place thenumbers in value order and find the middle number.
So here n=46 so Median position is average of 23rd and 24thvalue
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 wehave a pair of middle numbers, so the median isthe average of these two numbers:
Median=
c. The first quartile (or lower quartile or 25thpercentile) is the median of the bottom half of thenumbers. So, to find the first quartile, we need to placethe 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 75thpercentile) is the median of the upper half of thenumbers. So, to find the third quartile, we need to placethe 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
"Our Prices Start at $11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"
