Question

Victor collects data on the price of a dozen eggs at 8 different stores.

median: $ 1.55
Find the lower quartile and upper quartile of
the data set.
lower quartile: $
upper quartile: S
?
$1.39 $1.40 $1.44 $1.50 $1.60 $1.63 $1.65 $1.80

Answer 1

to find the lower quartile and upper quartile of the given dataset, we need to first arrange the data in ascending order:

$1.39, 1.40, 1.44, 1.50, 1.60, 1.63, 1.65, 1.80$

The median of the dataset is given as $1.55$. Since there are an even number of data points, the median is the average of the two middle values, which in this case are $1.50$ and $1.60$.

Now, we need to find the lower quartile and upper quartile. The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set.

The lower half of the dataset is $1.39, 1.40, 1.44, 1.50$. The median of this half is the average of the middle two values, which are $1.40$ and $1.44$.

Therefore, the lower quartile is $1.42$.

The upper half of the dataset is $1.60, 1.63, 1.65, 1.80$. The median of this half is the average of the middle two values, which are $1.63$ and $1.65$.

Therefore, the upper quartile is $1.64$.

Hence, the lower quartile of the dataset is $1.42$ and the upper quartile is $1.64$.

Answer 2

Lower quartile: $1.42

Upper quartile: $1.64

Explanation:

The median is the middle value when all data values are placed in order of size.

The ordered data set is:

$1.39 $1.40 $1.44 $1.50 $1.60 $1.63 $1.65 $1.80

There are 8 data values in the data set, so this is an even data set.

Therefore, the median is the mean of the middle two values:

`\implies \sf Median\;(Q_2)=(\$1.50+\$1.60)/(2)=\$1.55`

Place "||" in the middle of the data set to signify where the median is:

$1.39 $1.40 $1.44 $1.50 ║ $1.60 $1.63 $1.65 $1.80

The lower quartile (Q₁) is the median of the data points to the left of the median. As there is an even number of data points to the left of the median, the lower quartile is the mean of the the middle two values:

`\implies \sf Lower\;quartile\;(Q_1)=(\$1.40+\$1.44)/(2)=\$1.42`

The upper quartile (Q₃) is the median of the data points to the right of the median. As there is an even number of data points to the right of the median, the upper quartile is the mean of the the middle two values:

`\implies \sf Upper \;quartile\;(Q_1)=(\$1.63+\$1.65)/(2)=\$1.64`