Looking at the houses for sale in a certain city:

Question

Looking at the houses for sale in a certain city: 12 are listed at $300,000; 6 are listed at $400,000; 8 are listed at $500,000 and 2 are listed at $1,450,000.

a) Find the mean, median, and mode price of these houses for sale.

b) If most of the houses sell, except 8 houses (2 houses remain unsold at each price), find the mean, median, and mode sold price.

Answer 1

300000 400000 500000 1450000

300000 400000 500000 1450000

300000 400000 500000

300000 400000 500000

300000 400000 500000

300000 400000 500000

300000 500000

300000 500000

300000

300000

300000

300000

The easiest of the 3 (Mean, Median, and Mode) to answer right now just by looking at our lists of prices is the Mode. The number that occurs most frequently in the data set.

The MODE would be 300000.

The mean will be the sum of all of numbers listed divided by the number of numbers:

12(300000) + 6(400000) + 8(500000) + 2(1450000) = 3,600,000 + 2,400,000 + 4,000,000 + 2,900,000 =

12,900,000 ÷ (12 + 6 + 8 + 2) = 12,900,000/28 = 460,714.3

The MEAN is about 460,714.3

For the median, we have 28 numbers, so we will be locating the 2 middle numbers. 28 divided by 2 is 14, so...

There are 12 of the number 300,000 listed and then 6 of the number 400,000 listed. When we count into the middle from the lowest amounts we will land on the 2nd number 400,000 in the list.

Starting at the other end of the list, we have 2 numbers that are 1,450,000, 8 numbers that are 500,000; and 6 that are 400,000. So when we count to the 14th number in, we will land on 400,000 again, Both of the numbers we land on when we go to the middle are 400,000 so

The MEDIAN is 400,000.

Answer 2

Looking at the houses for sale in a certain city: 12 are listed at $300,000; 6 are listed at $400,000; 8 are listed at $500,000 and 2 are listed at $1,450,000.

a) Find the mean, median, and mode price of these houses for sale.

b) If most of the houses sell, except 8 houses (2 houses remain unsold at each price), find the mean, median, and mode sold price.

12:300000

8: 500000

6: 400000

2: 1, 450,000

For this problem and any problem where you are asked to find the mean, median, and mode, the easiest way is to list out all occurrences of each number from highest to lowest or lowest to highest.

The mean is the average, so add up all the numbers you have and divide by the total number of numbers in the set (in this case, divide the sum of all occurrences of each number by 28).

The median is the middle number. This is why it is important to list all numbers in number order. To find the middle number, cross off the highest and lowest number from your set of numbers. Do this until you reach the middle number (if your set has an odd number of values), or, in a case like this where you have an even number of values in the set, average the two middle values.

The mode is simply the number that occurs the most often. It is possible to have more than one mode in a set of numbers.