Math

QuestionDetermine if the mean or median better represents the center of the data set: 27, 25, 29, 27, 24, 30, 28, 24, 25, 28.

Studdy Solution

STEP 1

Assumptions1. We have a list of values27,25,29,27,24,30,28,24,25,28. We need to decide whether the mean or the median is a better measure of the center of the data set.

STEP 2

First, we need to calculate the mean of the data set. The mean is calculated by summing all the values and dividing by the count of values.
Mean=SumofallvaluesCountofvaluesMean = \frac{Sum\, of\, all\, values}{Count\, of\, values}

STEP 3

Now, plug in the given values to calculate the mean.
Mean=27+25+29+27+24+30+28+24+25+2810Mean = \frac{27+25+29+27+24+30+28+24+25+28}{10}

STEP 4

Calculate the mean value.
Mean=27710=27.7Mean = \frac{277}{10} =27.7

STEP 5

Next, we need to calculate the median of the data set. The median is the middle value when the data set is ordered from smallest to largest. If there is an even number of values, the median is the average of the two middle values.

STEP 6

First, order the data set from smallest to largest.
24,24,25,25,27,27,28,28,29,3024,24,25,25,27,27,28,28,29,30

STEP 7

Since we have an even number of values (10), the median is the average of the5th and6th values.
Median=5thvalue+6thvalue2Median = \frac{5th\, value +6th\, value}{2}

STEP 8

Plug in the5th and6th values to calculate the median.
Median=27+272Median = \frac{27 +27}{2}

STEP 9

Calculate the median value.
Median=542=27Median = \frac{54}{2} =27

STEP 10

Now that we have both the mean and the median, we can compare them. In this case, the mean and the median are very close to each other. This suggests that the data set is roughly symmetric and neither the mean nor the median is significantly affected by outliers. Therefore, both the mean and the median are good measures of the center of the data set. However, since the mean is slightly higher due to the influence of the higher values, the median might be a slightly better measure of the center for this data set.
The median is likely to be a better measure of the center of the data set.

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