Video: Finding the Median of a Data Set

Find the median of the values 13, 5, 9, 10, 2, and 15.

02:27

Video Transcript

Find the median of the values 13, five, nine, 10, two, and 15.

We can calculate the median of any data set by following two steps. Firstly, we put the numbers in ascending order. In this question, our six numbers in ascending order are two, five, nine, 10, 13, and 15. The median is the middle number. Therefore, we need to find the middle value from our list. One way to do this is to cross off a number from each end of the list. We cross off the highest number, 15, and the lowest number, two. We then cross off the next highest and next lowest, 13 and five. We are now left with two middle values, nine and 10.

To find the median in this case, we find the number that is halfway between the middle values. This can be calculated by adding the two middle values and then dividing by two. Nine plus 10 is equal to 19, and dividing this by two gives us 9.5. The median of the set of six values is therefore equal to 9.5. Half of our values must be above this, in this case, 10, 13, and 15. And half of the values must be below 9.5, nine, five, and two.

An alternative method here would’ve been to have found the median position. We do this using the formula 𝑛 plus one divided by two, where 𝑛 is the number of values. In this question, we had six values. We need to add six to one and divide by two. This is equal to 3.5. The median will therefore lie between the third and fourth value. As the third value was equal to nine and the fourth value 10, once again, we have proved that the median was 9.5.

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