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Find the median of the values 13, five, nine, 10, two, and 15.
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We can calculate the median of any data set by following two steps.
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Firstly, we put the numbers in ascending order.
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In this question, our six numbers in ascending order are two, five, nine, 10, 13, and 15.
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The median is the middle number.
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Therefore, we need to find the middle value from our list.
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One way to do this is to cross off a number from each end of the list.
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We cross off the highest number, 15, and the lowest number, two.
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We then cross off the next highest and next lowest, 13 and five.
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We are now left with two middle values, nine and 10.
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To find the median in this case, we find the number that is halfway between the middle values.
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This can be calculated by adding the two middle values and then dividing by two.
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Nine plus 10 is equal to 19, and dividing this by two gives us 9.5.
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The median of the set of six values is therefore equal to 9.5.
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Half of our values must be above this, in this case, 10, 13, and 15.
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And half of the values must be below 9.5, nine, five, and two.
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An alternative method here would’ve been to have found the median position.
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We do this using the formula 𝑛 plus one divided by two, where 𝑛 is the number of values.
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In this question, we had six values.
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We need to add six to one and divide by two.
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This is equal to 3.5.
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The median will therefore lie between the third and fourth value.
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As the third value was equal to nine and the fourth value 10, once again, we have proved that the median was 9.5.