Question

the data set below, what are the lower quartile, the median, and the upper quartile?
57 60 81 81 84 84 96

lower Q =
upper Q=
Median=

Answer 1

Answer:

lower Q = 57

upper Q= 96

Median=The median is the midpoint of a distribution. Half of the observations are smaller than the median and half are larger than the median. Because we have 95 observations (odd number), the median is the center observation in the ordered list. If the number of observations were even, then the median would be the mean of the two center observations in the ordered list. The position of the median in the ordered list is given by

\[\dfrac{(n+1)}{2}\]

Therefore, in our case, the position of the median is

\[\dfrac{(n+1)}{2} = \dfrac{95 + 1}{2} = 48\]

The 48th value in the ordered list is our median . Hence, the median is 80.

The first quartile is the median of the observations whose position in the ordered list are to the left of the location of the median. That means that the first quartile is the median of the new dataset the consists of all observations in “Exam 1” that are lower than the median.