What are the minimum, first quartile, median, mean, third quartile, and maximum of the following data set?: 10, 4, 9, 13, 5, 11, 5, 3, 7, 5

1 Answer
Jul 28, 2018

Minimum: 3

First quartile: 5

Median: 6

Third quartile: 10

Maximum: 13

Explanation:

First, let's list the data out from smallest to largest:
#3, 4, 5, 5, 5, 7, 9, 10, 11, 13#

The minimum is the lowest number in the data set.
Since we listed it out from smallest to largest, we know that the minimum is #3#.
# #

The median is the middle number. Cancel out #4# numbers from each side and we are left with #2# numbers:
#cancel(3), cancel(4), cancel(5), cancel(5), 5, 7, cancel(9), cancel(10), cancel(11), cancel(13)#

Find the average of the middle #2# numbers #5# and #7# to find the median:
#(5+7)/2 = 12/2 = 6#
Therefore, the median is #6#.
# #

The first quartile (Q1) is the median of the lower half of data which lies at 25% of the data.
Let's look at the lower half of numbers:
#3, 4, 5, 5, 5#

Cancel out #2# numbers from each side and we are left with the #Q1#:
#cancel(3), cancel(4), 5, cancel(5), cancel(5)#
Therefore, the #Q1# is #5#.
# #

The third quartile (Q3) is the median of the upper half of data which lies at 75% of the data.

Let's look at the upper half of numbers:
#7, 9, 10, 11, 13#

Again cancel out #2# numbers from each side:
#cancel(7), cancel(9), 10, cancel(11), cancel(13)#

The #Q3# is #10#.
# #

The maximum is the highest number in the data set; it is #13#.

Hope this helps!