The table shows the number of artifacts found by each member of an expedition during an excavation at a historical site. Find the range and interquartile range of the data. Expedition member Matthew found five artifacts. Natalie found four artifacts. Chloe found five. Charlotte found five. Jacob found six. Daniel found five. And William found 10.
In order to find the range and interquartile range, we need to put our number of artifacts found by each member in ascending order, which means we need to order our numbers from least to greatest — smallest to largest. Natalie found four, Matthew, Chloe, Charlotte, and Daniel all found five, Jacob found six, and William found 10. So these are now in ascending order.
In order to find the range, we need to take the largest number and then subtract the smallest number. So the range is equal to 10 minus four, which is six. So the range tells us how far apart the smallest number and the largest number are. There’s a difference of six between them.
In order to find the interquartile range, we need to take the upper quartile and subtract the lower quartile. So how do we find these quartiles. We’ll begin with finding the median — the middle number. Since there are seven total numbers, the fourth one will be the middle one — the median — because now there are three numbers on each side of it. It’s in the middle.
So the quartiles will be the middle of these sets. So the middle of four, five, and five would be five because out of three numbers, the second one will be in the middle. So again, five will be our lower quartile. And then out of the three on the top, the second one will be in middle. So again, out of three numbers, the second one is in the middle. So six is our upper quartile.
So our interquartile range is our upper quartile minus our lower quartile. So six minus five, which is one. So the upper quartile and the lower quartile only one value apart. So once again, the range is six and the interquartile range is one.