14 , 15 , 3 , 15 , 14 , 14 , 18 , 15 , 8 , 16
Let's proceed to finding the mean, median, and mode.
Mean
The mean of a data set x is calculated by finding the sum of all of the values in the set and then dividing by the number of values in the set. In this case, there are 10 values in the set.
When the data are arranged in numerical order, the median is the middle value — or the mean of the two middle values. Let's arrange the given values and find the median.
3 , 8 , 14 , 14 , 14 | 15 , 15 , 15 , 16 , 18
Since there are 10 values, there is no one middle value. Therefore, the median is the mean of the two middle values.
Median: 14+ 15/2=14.5
Mode
The mode is the value or values that appear most often in a set of data.
Let's find the mode of the given values.
14 , 15 , 3 , 15 , 14 , 14 , 18 , 15 , 8 , 16
Since the data set has two values that appear more often than the other values but equally as often as each other, there are two modes.
Modes: 14and15
b There are two modes in this set. Therefore, it is not the measure that best represents the data.
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Mode & Median & Mean
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Let's now consider the mean and the median. In the given list of numbers, 3 is a value that is way lower than the rest. This value can be considered an outlier. Outliers affect the mean but not the median. Therefore, since it is pulled down by the outlier, the mean is not the measure that best represents the data. Conversely, the median is the measure that best represents the data.
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Mode & Median & Mean
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