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$155 $267 $284 $194 $299 $284 $287 $179 What is the mean, median, and mode of this data set?

1 Answer

1 vote

Answer:

Mean = 243.625

Median = 275.5

Mode = 284

Each value is exact without any rounding.

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Original data set:

$155 $267 $284 $194 $299 $284 $287 $179

Let's remove the dollar signs, and separate each item with a comma:

155,267,284,194,299,284,287,179

Then sort the values from lowest to highest.

155,179,194,267,284,284,287,299

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To find the mean, we add up the values and divide by n = 8 since there are 8 items in the list.

(155+179+194+267+284+284+287+299)/8 = 243.625 is the mean

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Refer to the sorted data set.

The median is the middle-most value. Because the sample size n = 8 is even, we'll have two values tied for the middle.

n/2 = 8/2 = 4

The items in slot 4 and 5 are tied for the middle.

The values in slot 4 and 5 are 267 and 284 in that exact order.

Compute the midpoint: (267+284)/2 = 275.5 is the median

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The mode is the most frequent value. Look through the sorted data set to see that 284 shows up twice. This is the most frequent compared to the other values (that show up only once).

Therefore, the mode is 284

Side note: It's possible to have multiple modes. It's also possible to not have any modes at all.

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