Question

Sally Reynolds sells real estate along the coastal area of Northern California. Below are her total annual commissions between 2007 and 2017.

Year	Amount (thousands)
2007	292.16
2008	233.80
2009	206.97
2010	202.67
2011	164.69
2012	206.53
2013	237.51
2014	225.57
2015	255.33
2016	248.14
2017	269.11

Click here for the Excel Data File

Find the mean, median, and mode of the commissions she earned for the 11 years. (Round your answers to 2 decimal places.)

Answer 1

We are given data:

Year	Amount (thousands)
2007	292.16
2008	233.8
2009	206.97
2010	202.67
2011	164.69
2012	206.53
2013	237.51
2014	225.57
2015	255.33
2016	248.14
2017	269.11

We have to find the mean, median and mode for the given commissions.

Mean is the average value of the data which can be used as the representative of the whole given data.

It is calculated as:

The total sum of the observations is divided by the number of observations.

Mathematically written as:

where denotes the position of the observation

denotes the value of the observations

Thus, let us calculate this:

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Now, we have to find the median.

Median is the value of the data observations which divides the whole data into two equal parts such that the number of observations above it equals the number of observations below it.

Calculation Procedure:

• First of all, arrange the data in ascending order or descending order.
• Next count the number of observations in the data,
  • If n= odd, then it is simply that the middlemost observation would be the median of the data.
  • If n = even, then there would be two middle observations we get, for getting median we take the average of both the observations, The resultant figure would be the median of the data.

Let us calculate the median,

firstly 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

Now, the number of observations, n= 11 which is odd,

So, the middle observation would be at the 6th position

Thus, the median =

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Now,

Mode is the value of the observation which occur the most number of ties in the whole data.

In other words, the value of the observations having the highest frequency.

Frequency means the number of times a value occurs in the data.

In the given data, we can see that none of the observations is repeated more with respect to each other or it can be said that each observation has an equal frequency which is 1.

None of the observations has the highest frequency.

Thus, the given data has no mode.

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