Nine homes recently sold in your community in the following

Nine homes recently sold in your community in the following order and for these amounts: $360,000; $460,000; $360,000; $380,000; $360,000; $420,000; $380,000; $520,000; and $360,000. Your boss, Andrew Santoso, a realtor with Hagen & Associates, wants you to compute the mean, median, and mode for this real estate market.

Compute the mean, median, and mode for the recently sold homes. Explain your analysis as well as the characteristics of each type of “average.”

Solution

Mean = Sum of all values / Number of values =

[ 360,000+460,000+360,000+380,000+360,000+420,000+380,000+520,000+360,000.] / 9

= 3600000 / 9 = $ 400,000

Median .......... For computing the median .... arrange the given values in assending order

360,000, 360,000, 360,000, 360,000, 380,000, 380,000, 420,000, 460,000 and 520,000

Now ........ compute ( n + 1 ) / 2 = (9+1) / 2 = 5th term of above series is the median value of homes sold

= 380,000

Mode = The value that had maximum recurring in the series of observations.

Mode value = 360,000

Explanation

Mean or arthematic mean is widely used type of average. But it had the tendency of being effected by very small values and very high values. Such non represantative values will effect the true average. In such situations we use, positional average called median. Mode is specific and limited application model for average, where only one value out of given is to be choosen as average. Most repeated value is model value.

Thus each of these averages had their unique merits and demerits, hence careful analysis is to be done in choosing the correct type of average in each of the circumstances.