7. My Noles Ask Your Teuche groups was at most 6 hours. The aocompanying data wa
ID: 3369630 • Letter: 7
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7. My Noles Ask Your Teuche groups was at most 6 hours. The aocompanying data was read from a omparative boxplot in an article ED 0 0.1 01 0.1 01 0.2 0.2 U.3 0.3 0.3 0.4 U.SU./ U.? 1.0 1.5 2.9 2.9 3.4 4.? 8.y 9.3 11.0 20.0 0 01 o.l 0.1 0. 0.2 0.2 0.2 0.3 0.3 03 0. 0. 0.3 0.G 0.8 0.0 1.0 1.2 14 1. 17 2.0 3.2 3.5 41 4.3 4.8 .O 5.65. 6.0 1. 127 14.0 16.6 17.A (a Determine the median, fourths, and fourth spread Tor the EO sample. lower tourth upper fourth fourth spread Detemine he median, fourths, an fourth spread or Uhe on ED sample, median ower fourth0.3 upner tourth tourth spread 5Explanation / Answer
The median is the value separating the higher half of a data sample from the lower half (or middle value if the data is arranged in ascending order).
Order the n observations ascendingly and separate the smallest half from the largest half. Then the lower (upper) fourth is the median of the smallest (largest) half.
A measure of spread, the fourth spread = upper fourth – lower fourth
(a) for ED sample
Median = 0.4
lower half data set : 0 0 0 0 0.1 0.1 0.1 0.1 0.2 0.2 0.3 0.3 0.3 0.4
total 14 values so median is average of 7th and 8th value
median of this data set = (0.1+0.1)/2 = 0.1
so,lower fourth = 0.1
upper half data set : 0.4 0.5 0.7 0.8 1.0 1.5 2.8 2.9 3.4 4.0 8.8 9.3 11.6 20.0
total 14 values so median is average of 7th and 8th value
median of this data set = (2.8+2.9)/2 = 2.85
so,lower fourth = 2.85
fourth spread = 2.85-0.1 = 2.75
For Non ED sample
total 50 values so median is average of 25th and 26th value
Median = (1.5+1.7)/2=1.6
lower half data set : 0 0 0 0 0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.4 0.5 0.6 0.8 0.9 1.0 1.2 1.4 1.5
total 25 values so median is 13th value
median of this data set = 0.3
so,lower fourth = 0.3
upper half data set : 1.7 2.0 3.2 3.5 4.1 4.3 4. 8 5.0 5.6 5.9 6.0 6.3 7.7 8.2 8.8 9.1 9.7 9.9 11.0 11.5 12.2 12.7 14.0 16.6 17.8
total 25 values so median is 13th value
median of this data set = 7.7
so,lower fourth = 7.7
fourth spread = 7.7-0.3 = 7.4
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