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Math  /  Data & Statistics

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The prices of 9 houses sold in a neighborhood are shown. Complete parts (a) through (e) below. \begin{tabular}{ll} $199,000\$ 199,000 & $210,000\$ 210,000 \\ $171,000\$ 171,000 & $185,000\$ 185,000 \\ $220,000\$ 220,000 & $188,000\$ 188,000 \\ $17,000\$ 17,000 & $190,000\$ 190,000 \\ $485,000\$ 485,000 & \end{tabular} A. The mode of the data set is $\$ □\square (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There is no mode. d) Determine the midrange.
The midrange of the data set is $328,000\$ 328,000. (Type an integer or a decimal.) e) Which measure of central tendency, the mean or the median, best represents the typical price of the houses sold?
The best measure of central tendency that represents the typical price of the houses sold is the mean □\square because the mean is not affected by unusual data values.

Studdy Solution

STEP 1

1. The data set consists of the following house prices: 199,000,210,000,171,000,185,000,220,000,188,000,17,000,190,000,485,000199,000, 210,000, 171,000, 185,000, 220,000, 188,000, 17,000, 190,000, 485,000.
2. The mode is the value that appears most frequently in the data set.
3. The midrange is the average of the maximum and minimum values in the data set.
4. The mean is the arithmetic average of the data set.
5. The median is the middle value when the data set is ordered.

STEP 2

1. Identify the mode of the data set.
2. Determine the midrange of the data set.
3. Evaluate which measure of central tendency best represents the typical price of the houses sold.

STEP 3

List the data points:
199,000,210,000,171,000,185,000,220,000,188,000,17,000,190,000,485,000 199,000, 210,000, 171,000, 185,000, 220,000, 188,000, 17,000, 190,000, 485,000

STEP 4

Check for the mode by identifying any repeating values in the data set. Since all values are unique, there is no mode.

STEP 5

Order the data points to find the minimum and maximum values:
17,000,171,000,185,000,188,000,190,000,199,000,210,000,220,000,485,000 17,000, 171,000, 185,000, 188,000, 190,000, 199,000, 210,000, 220,000, 485,000

STEP 6

Identify the minimum value (\$17,000) and the maximum value (\$485,000).

STEP 7

Calculate the midrange:
Midrange=(Minimum value+Maximum value)2=(17,000+485,000)2=251,000 \text{Midrange} = \frac{(\text{Minimum value} + \text{Maximum value})}{2} = \frac{(17,000 + 485,000)}{2} = 251,000

STEP 8

Evaluate the mean and median to determine the best measure of central tendency. Calculate the mean:
Mean=(199,000+210,000+171,000+185,000+220,000+188,000+17,000+190,000+485,000)9 \text{Mean} = \frac{(199,000 + 210,000 + 171,000 + 185,000 + 220,000 + 188,000 + 17,000 + 190,000 + 485,000)}{9}
Mean=1,865,0009=207,222.22 \text{Mean} = \frac{1,865,000}{9} = 207,222.22

STEP 9

Identify the median, which is the 5th value in the ordered list:
Median=190,000 \text{Median} = 190,000

STEP 10

Compare the mean and median. The median is less affected by the outlier (\$485,000) than the mean. Therefore, the median better represents the typical price of the houses sold.
The mode is: No mode
The midrange is: \$251,000
The best measure of central tendency is the median because it is less affected by unusual data values.

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