For each sets of the data find the:

Question

find the mean, median, mode, range, first quartile, second quartile, IQR and sigma

The Number of Hours Jim Sleeps Each week:

36, 37, 38, 34, 30, 28, 28, 39, 40, 45

Answer 1

n = number of values = 10

the mean is the sum of the numbers divided by the number of values

put the values in ascending order.

to find the median

the location of the number for the xth percentile is x/100 * (n + 1)

The median is the 50th percentile, so the location is 50/100 ( 11) = 5.5.

Since the location is not an integer, the median is the average of the 5th and 6th values.

the mode is the most often occurring values of those values which occur more than once.

the range is the maximum value - minimum value.

the first quartile is the 25th percentile, so the location is 25/100 (11) = 2.75

Since the location is not an integer, the 1st quartile is the average of the 2nd and 3rd values.

the second quartile is the median.

since you want to find the IQR, you need to find the 3rd quartile.

the third quartile is the 75th percentile, so the location is 75/100 * (11) = 8.25

Since the location is not an integer, the 3rd quartile is the average of the 8th and 9th values.

the IQR is the difference between the 3rd and 1st quartile values.

sigma is the standard deviation which is equal to sum (x(i) - mean)^2/ (n - 1), where i goes from 1 to 10.