5.5 Averages and probability  (Page 3/9)

Find the median of $12,13,19,9,11,15,\text{and}18.$

Solution

List the numbers in order from smallest to largest.	9, 12, 13, 15, 18, 19
Count how many numbers are in the set. Call this $n$ .	$n=7$
Is $n$ odd or even?	odd
The median is the middle value.
The middle is the number in the 4th position.	So the median of the data is 13.

Got questions? Get instant answers now!

Got questions? Get instant answers now!

Kristen received the following scores on her weekly math quizzes:

$83,79,85,86,92,100,76,90,88,\text{and}64.$ Find her median score.

Solution

Find the median of 83, 79, 85, 86, 92, 100, 76, 90, 88, and 64.
List the numbers in order from smallest to largest.	64, 76, 79, 83, 85, 86, 88, 90, 92, 100
Count the number of data values in the set. Call this $\mathrm{n.}$	$n=10$
Is $n$ odd or even?	even
The median is the mean of the two middle values, the 5th and 6th numbers.
Find the mean of 85 and 86.	$\text{mean}=\frac{85+86}{2}$
	$\text{mean}=85.5$
	Kristen's median score is 85.5.

Got questions? Get instant answers now!

Got questions? Get instant answers now!

Identify the mode of a set of numbers

The average is one number in a set of numbers that is somehow typical of the whole set of numbers. The mean and median are both often called the average. Yes, it can be confusing when the word average refers to two different numbers, the mean and the median! In fact, there is a third number that is also an average. This average is the mode    . The mode of a set of numbers is the number that occurs the most. The frequency , is the number of times a number occurs. So the mode of a set of numbers is the number with the highest frequency.

Suppose Jolene kept track of the number of miles she ran since the start of the month, as shown in [link] .

If we list the numbers in order it is easier to identify the one with the highest frequency.

Jolene ran $8$ miles three times, and every other distance is listed only once. So the mode of the data is $8$ miles.

The ages of students in a college math class are listed below. Identify the mode.

$18,18,18,18,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,22,23,24,24,25,29,30,40,44$

Solution

The ages are already listed in order. We will make a table of frequencies to help identify the age with the highest frequency.

Now look for the highest frequency. The highest frequency is $7,$ which corresponds to the age $20.$ So the mode of the ages in this class is $20$ years.

Got questions? Get instant answers now!

Got questions? Get instant answers now!

The data lists the heights (in inches) of students in a statistics class. Identify the mode.

$56$	$61$	$63$	$64$	$65$	$66$	$67$	$67$
$60$	$62$	$63$	$64$	$65$	$66$	$67$	$70$
$60$	$63$	$63$	$64$	$66$	$66$	$67$	$74$
$61$	$63$	$64$	$65$	$66$	$67$	$67$

Solution

List each number with its frequency.

Now look for the highest frequency. The highest frequency is $6,$ which corresponds to the height $67$ inches. So the mode of this set of heights is $67$ inches.

Got questions? Get instant answers now!

Got questions? Get instant answers now!