Billy’s math test scores are 90, 92, 69, 76, 93, and 84. Find the range and interquartile range of his scores.
First, we list numbers from least to greatest. Our next step would be to find the median. Now, there are six numbers here, which means a middle number wouldn’t really be listed. So we’re gonna have to find it. So what number is in the middle of 84 and 90? That would be 87. So 87 is our median; it’s the middle of this list.
Next, we find the quartiles: the lower quartile and upper quartile. Now to the left of the median, there are three numbers. So 76 is our lower quartile. To the right of our median, there are three numbers; that means 92 is our upper quartile.
Now we have everything that we need to answer our question. It says, “Find the range and the interquartile range of his scores.” In order to find the range, we simply subtract the largest number and the smallest number. So 93 minus 69, which means our range is 24.
The interquartile range is where you take the upper quartile and subtract the lower quartile, which would be 92 minus 76. So our interquartile range would be 16.