### 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 π three
minus π 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 donβt 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 π 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.