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Big Ideas Math Algebra 2, 2014

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Big Ideas Math Algebra 2, 2014 View details

Maintaining Mathematical Proficiency

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Exercise 3 Page 593

It may be easier to calculate the mean, median, and mode if you rearrange the numbers first.

Mean: about 19.8
Median: 16
Mode: 44
Which Measure Is Best? Median. The mean and mode are both greater than most of the data.

Practice makes perfect

The first thing that should be done when finding the key features of a data set is rearranging the numbers from least to greatest. 1, 11, 12, 15, 16, 17, 18, 44, 44 Let's proceed to finding the mean, median, and mode.

Mean

The mean of a data set is calculated by finding the sum of all values in the set and then dividing by the number of values in the set. In this case, there are 9 values in the set.

Mean=Sum of values/Number of values

SubstituteValues

Substitute values

Mean=1+ 11+12+ 15+16+17+18+44+44/9

Add terms

Mean=178/9

Calculate quotient

Mean=19.7

Round to 1 decimal place(s)

Mean≈19.8

Median

To identify the median, we observe the middle value. 1, 11, 12, 15, 16, 17, 18, 44, 44 We can see that the middle value in this set is 16, so this is our median.

Mode

The mode of a data set is the value that occurs most frequently. 1, 11, 12, 15, 16, 17, 18, 44, 44 We can see that 44 occurs more frequently than the other values, so there is one mode in this set.

Which Measure Is Best?

Recall that the mean is highly influenced by values that are way greater or smaller than the rest of the values. Therefore, since 44 is much greater than the rest of the values, the mean is not a good measure of the data. In this case, the best measure is the median. Another good measure would be the mode because it occurs the most frequently within the data.

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Exercises p.593