Question

Sally Reynolds sells real estate along the coastal area of Northern California. Below are her total annual commisions between 2002 and 2012. Find the mean, median, and mode of the commissions she earned for the 11 years.Year Amount(thousands)2002 $237.512003 $233.802004 $206.972005 $248.142006 $164.692007 $292.162008 $269.112009 $225.572010 $255.332011 $202.672012 $206.53

Answer 1

Mean of the commissions she earned for the 11 years is $231.13.

Median of the commissions she earned for the 11 years is $233.8.

Mode of the data can be any number from the given amounts.

Explanation:

The given data table is

Year Amount(thousands)

2002 $237.51

2003 $233.80

2004 $206.97

2005 $248.14

2006 $164.69

2007 $292.16

2008 $269.11

2009 $225.57

2010 $255.33

2011 $202.67

2012 $206.53

Mean of the commissions is

`Mean=(\sum x)/(n)`

`Mean=(237.51+233.80+206.97+248.14+164.69+292.16+269.11+225.57+255.33+202.67+206.53)/(11)`

`Mean=231.1345\approx 231.13`

Mean of the commissions she earned for the 11 years is $231.13.

The given data set is

237.51, 233.80, 206.97, 248.14, 164.69, 292.16, 269.11, 225.57, 255.33, 202.67, 206.53

Arrange the data in ascending order.

164.69, 202.67, 206.53, 206.97, 225.57, 233.8, 237.51, 248.14, 255.33, 269.11, 292.16

Median of the data is middle term of the data set.

So, median of the data is $233.8.

Most frequently accruing number is known as mode of the data.

In the given data set all amount have same frequency, which is 1. So, mode of the data can be any number from the given amounts.