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QuestionFind the sum of the weighted average and the mode of these home costs: 6 homes at \$65000, 8 homes at \$85000, 6 homes at \$105000.

Studdy Solution

STEP 1

Assumptions1. Six homes cost 65,000each.Eighthomescost65,000 each. Eight homes cost 85,000 each3. Six homes cost $105,000 each4. The weighted average is calculated by multiplying each value by its frequency, summing these products, and then dividing by the total frequency.
5. The mode is the most frequently occurring value in a data set.

STEP 2

First, we need to calculate the total cost of each group of homes. We can do this by multiplying the cost of each home by the number of homes in that group.
For the homes costing 65,00065,000Total_cost_1=Number_of_homes_1timesCost_of_each_home_1Total\_cost\_1 = Number\_of\_homes\_1 \\times Cost\_of\_each\_home\_1$

STEP 3

Now, plug in the given values for the number of homes and the cost of each home to calculate the total cost of the first group of homes.
Total_cost_1=6times$65,000Total\_cost\_1 =6 \\times \$65,000

STEP 4

Calculate the total cost of the first group of homes.
Total_cost_1=6times$65,000=$390,000Total\_cost\_1 =6 \\times \$65,000 = \$390,000

STEP 5

Repeat the same steps for the homes costing 85,000and85,000 and 105,000.
Total_cost_2=Number_of_homes_2timesCost_of_each_home_2Total\_cost\_2 = Number\_of\_homes\_2 \\times Cost\_of\_each\_home\_2Total_cost_2=8times$85,000=$680,000Total\_cost\_2 =8 \\times \$85,000 = \$680,000Total_cost_3=Number_of_homes_3timesCost_of_each_home_3Total\_cost\_3 = Number\_of\_homes\_3 \\times Cost\_of\_each\_home\_3Total_cost_3=times$105,000=$630,000Total\_cost\_3 = \\times \$105,000 = \$630,000

STEP 6

Now, we can calculate the weighted average. This is done by summing the total costs of each group of homes and dividing by the total number of homes.
Weighted_average=Total_cost_1+Total_cost_2+Total_cost_3Total_number_of_homesWeighted\_average = \frac{Total\_cost\_1 + Total\_cost\_2 + Total\_cost\_3}{Total\_number\_of\_homes}

STEP 7

Plug in the values for the total costs and the total number of homes to calculate the weighted average.
Weighted_average=$390,000+$680,000+$630,0006++6Weighted\_average = \frac{\$390,000 + \$680,000 + \$630,000}{6 + +6}

STEP 8

Calculate the weighted average.
Weighted_average=$1,700,00020=$85,000Weighted\_average = \frac{\$1,700,000}{20} = \$85,000

STEP 9

The mode is the most frequently occurring value in a data set. In this case, the mode is the cost of the homes that occur most frequently.Looking at our data, we see that eight homes cost 85,000,whichisthehighestfrequency.Therefore,themodeis85,000, which is the highest frequency. Therefore, the mode is 85,000.

STEP 10

Finally, we can calculate the sum of the weighted average and the mode.
Sum=Weighted_average+ModeSum = Weighted\_average + Mode

STEP 11

Plug in the values for the weighted average and the mode to calculate the sum.
Sum=$85,000+$85,000Sum = \$85,000 + \$85,000

STEP 12

Calculate the sum.
Sum=$85,000+$85,000=$170,000Sum = \$85,000 + \$85,000 = \$170,000The sum of the weighted average and the mode of these homes' costs is $170,000.

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