Question

Sally Reynolds sells real estate along the coastal area of Northern California. Below are her total annual commissions between 2002 and 2012.

Year Amount (thousands)

2002 $236.09

2003 204.43

2004 253.82

2005 268.4

2006 231.15

2007 205.7

2008 262.18

2009 162.77

2010 268.4

2011 224.45

2012 205.17

Find the mean, median, and mode of the commissions she earned for the 11 years.

Answer 1

Mean = $229.32

Median = $231.15

Mode = $268.4

Explanation:

Mean = the average.

The average is the sum of variables divided by the number of variables.

x = each variable

N = number of variables = 11

Average = (Σx)/N = (236.09 + 204.43 + 253.82 + 268.4 + 231.15 + 205.7 + 262.18 + 162.77 + 268.4 + 224.45 + 205.17)/11

Mean = 2522.56/11 = $229.32

b) Median is the value that falls at the middle of the data set if all the variables are arranged in ascending or descending order.

So, to find the Median, we first arrange the variables in ascending order.

162.77

204.43

205.17

205.70

224.45

231.15

236.09

253.82

262.18

268.4

268.4

Since there are 11 variables, the Median is the number that falls at the middle of the distribution, that is, at the sixth position.

Median = $231.15

c) Mode is the number that appears the most in a distribution.

In this distribution, only 268.4 appears more than once.

Hence, the more is $268.4