### Video Transcript

The table describes how many
minutes a day an eight- to nine-month-old baby is awake. The greatest time is 208 minutes,
the lower quartile is 172 minutes, the median is 186 minutes, the interquartile
range is 24 minutes, and the range is 56 minutes. Part a) Draw a box plot for this
summary data. The second box plot shows how many
minutes a day a 10- to 12-month-old baby is awake. Part b) Compare the distribution of
times an eight- to [nine-] month-old is awake to the distribution of times a 10- to
12-month-old is awake.

In order to draw a box plot, we
need five bits of information: the greatest time, the least time, the lower
quartile, the upper quartile, and the median. The lowest time can be calculated
by subtracting the range from the greatest time — in this case subtracting 56 from
208. This is equal to 152. We can calculate the upper quartile
by adding the interquartile range to the lower quartile — in this case adding 24 to
172. This is equal to 196. Therefore, the upper quartile is
196.

In order to draw the box plot, we
mark these five key points. The lowest value was 152 minutes,
the lower quartile was 172 minutes, the median was 186 minutes, the upper quartile
196 minutes, and the greatest value 208 minutes. Now that we have completed part a,
we need to consider the second box plot which shows how many minutes a day a 10- to
12-month-old baby is awake.

In order to compare the two
distributions, we’re going to look at two key bits of information. Firstly, we are gonna compare the
medians. The median for the eight- to
nine-month-olds was 186 minutes and the median for the 10- to 12-month-olds was 210
minutes. As this median time for the 10- to
12-month-olds is higher, they are awake for longer on average.

The second bit of information that
we will use to compare the distributions is the interquartile range. The interquartile range for the
eight- to nine-month-olds was 24 minutes. To calculate the interquartile
range for the 10- to 12-month-olds, we subtract the lower quartile from the upper
quartile — in this case 226 minus 188. This is equal to 38. As the interquartile range is
greater for the 10- to 12-month-olds, we can say that the time that they are awake
is more varied or more spread out.

The two box plots enable us to make
two conclusions. Firstly, the 10- to 12-month-olds
are awake for longer on average. And secondly, as their
interquartile range is higher, the amount of time they are awake for is more
varied.