Cost per serving (in cents) for six high-fiber cereals rated very good and for n
ID: 3207128 • Letter: C
Question
Cost per serving (in cents) for six high-fiber cereals rated very good and for nine high-fiber cereals rated good by a magazine are shown below.
Cereals Rated Very Good 47 49 64 42 19 76
Cereals Rated Good 72 30 53 53 69 43 48 27 54
Combining the cost-per-serving data for high-fiber cereals rated very good and those rated good from above gives the following data set. 47 49 64 42 19 76 72 30 53 53 69 43 48 27 54
(a) Compute the quartiles and the interquartile range for this combined data set.
lower quartile =
upper quartile =
interquartile range =
(b) Compute the interquartile range for just the cereals rated good.
Show me the steps please
Explanation / Answer
a.
he 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.
19 27 30 42 43 47 48 49 53 53 54 64 69 72 76
So, the bottom half is
19 27 30 42 43 47 48
The median of these numbers is 42.
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.
19 27 30 42 43 47 48 49 53 53 54 64 69 72 76
So, the upper half is
53 53 54 64 69 72 76
The median of these numbers is 64.
The interquartile range is the difference between the third and first quartiles.
The third quartile is 64.
The first quartile is 42.
The interquartile range = 64 - 42 = 22.
b.
The interquartile range is the difference between the third and first quartiles.
The third quartile is 61.5.
The first quartile is 36.5.
The interquartile range = 61.5 - 36.5 = 25.