Question

Find the mean, the median, and the mode of the collection of numbers. $$\begin{aligned}&5,3,10,13,8,18,5,17,2\\\&7,9,10,4,1\end{aligned}$$

Short answer

The mean of the data set is 8.21, the median is 8, and the modes are 5 and 10.

Step-by-step solution

Order the Data Ascendingly

First, we arrange the given data set in ascending order: \(1, 2, 3, 4, 5, 5, 7, 8, 9, 10, 10, 13, 17, 18\). This step is important as it allows easier calculation of the mean, median, and mode.

Calculate The Mean (Average)

The mean, also known as the average, of a data set is calculated by adding all values in the set together and then dividing by the number of values in the set. The given data set has 14 values, so we sum the numbers and divide by 14. \[ Mean = \frac{1+2+3+4+5+5+7+8+9+10+10+13+17+18}{14} = 8.21 \]

Calculate The Median

The median, or middle value, of a data set is found by arranging the data set from lowest to highest and finding the number in the exact middle. With an even number of values (14 in this case), the two middle values need to be found and averaged. Here, those two numbers are 7 and 9. \[ Median = \frac{7 + 9}{2} = 8 \]

Calculate The Mode

The mode, or most frequently occurring value, of a data set is found by identifying which number appears most often in the set. In this set, the numbers 5 and 10 each appear twice, more than any other number, so they are the modes.