Question

The table shows the number of servings of fruits and vegetables that Cole eats in one week. Find the range, median, lower quartile, and upper quartile.

Short answer

Range is 5

Median is 5

Lower quartile is$Q_1=3$

Lower quartile is$Q_3=7$

Step-by-step solution

Step-1. Apply the concept of range, median, lower quartile, and upper quartile.

• The range is the difference between the largest observation and the smallest observation of a data set.
• The median is the middle value when a data set is ordered from least to greatest. It is the second quartile (Q2) and divides the data into two-half.

• The lower quartile Q1 is the median of the lower half of the data.
• The upper quartile Q3is the median of the upper half of the data.

• If the size of the data set is odd, include the median when finding the first and third quartiles.
• If the size of the data set is even, the median splits the data set into lower and upper halves.

Step-2. Calculation of range.

Given data for 7 days:

$\left\{5,7,5,4,3,3,8\right\}$

Arrange the data set in ascending order:

3,3,4,5,5,7,8

$\begin{array}{l}\mathrm{Range}=\mathrm{Largest}-\mathrm{Smallest}\\ \Rightarrow \mathrm{Range}=8-3\\ \Rightarrow \mathrm{Range}=5\end{array}$

Step-3. Calculation of median.

Given data for 7 days:

$\left\{5,7,5,4,3,3,8\right\}$

Arrange the data set in ascending order:

3,3,4,5,5,7,8

So, the median is average of ${\left(\frac{7+1}{2}\right)}^{th}=4^{th}$and $5^{th}$observation

Therefore, the median is$Q_2=5$

Step-4. Calculation of lower quartile.

Given data for 7 days:

$\left\{5,7,5,4,3,3,8\right\}$

Arrange the data set in ascending order:

3,3,4,5,5,7,8

From step 3, the median of the data set is 5

Hence, the lower half of the data set is:

3,3,4

The lower quartile is the median of lower half of the data set:

$Q_1=3$

Step-5. Calculation of upper quartile.

Given data for 7 days:

$\left\{5,7,5,4,3,3,8\right\}$

Arrange the data set in ascending order:

3,3,4,5,5,7,8

From step 3, the median of the data set is 5

Hence, the upper half of the data set is:

5,7,8

The upper quartile is the median of upper half of the data set:

$Q_3=7$