Video: Finding the Range and Interquartile Range of a Data Set in a Frequency Table

The table shows some non-English languages spoken by some of the US population. Determine the range and interquartile range of the data.

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Video Transcript

The table shows some non-English languages spoken by some of the U.S. population. Determine the range and interquartile range of the data.

The range of any data set can be calculated by subtracting the minimum value from the maximum. Whereas the interquartile range or IQR is equal to the upper quartile minus the lower quartile, also known as 𝑄 three minus 𝑄 one. Our first step is to sort our eight values into ascending order. The smallest value is equal to 216,300. This is the number of people that speak Hebrew. Next, we have 246,900 people that speak Armenian. We can continue to list these in order all the way up to the number of Spanish speakers, which is 37,580,000.

This is the maximum value. We can now calculate the range by subtracting the minimum value from the maximum one. This is equal to 37,363,700. This is the range of the data in the frequency table. As we have eight values in total, and the median is the middle number, this will lie halfway between the fourth and fifth value. Whilst we don’t need the median to calculate the interquartile range, it makes it easier to find the lower and upper quartiles.

The lower quartile is the center of the bottom half of our data. As there are four values that are less than the median, the lower quartile will lie halfway between 246,900 and 304,900. We can find the midpoint of these two values by adding them and then dividing by two. This gives us 275,900. We can repeat this process for the upper quartile or 𝑄 three. As there are four values above the median, the center of this will lie halfway between 800,000 and 1,410,000. This is equal to 1,105,000. We can then calculate the interquartile range by subtracting 275,900 from this. This is equal to 829,100, which is the interquartile range of the data.

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