Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.

this data set represents the number of cups of coffee sold in a café between 8 a.m. and 10 a.m. every day for 14 days.

\\{10, 9, 6, 12, 4, 6, 7, 8, 15, 14, 12, 9, 10, 5\\}.

the difference of the values of the first and third quartiles of the data set is .

Explanation:

⚡ Using what you learned: Interquartile Range (IQR)

Step 1: Order the data set

Arrange the 14 data points in ascending order:

$$ 4, 5, 6, 6, 7, 8, 9, 9, 10, 10, 12, 12, 14, 15 $$

Step 2: Find the median (Q2)

Since there are 14 data points, the median is the average of the 7th and 8th values:

$$ \text{Median} = \frac{9 + 9}{2} = 9 $$

This splits the data into two halves:

• Lower half (first 7 values): \( \{4, 5, 6, 6, 7, 8, 9\} \)
• Upper half (last 7 values): \( \{9, 10, 10, 12, 12, 14, 15\} \)

Step 3: Find the first quartile (Q1) and third quartile (Q3)

The first quartile (\( Q_1 \)) is the median of the lower half:

$$ Q_1 = 6 $$

The third quartile (\( Q_3 \)) is the median of the upper half:

$$ Q_3 = 12 $$

Step 4: Calculate the difference (IQR)

Subtract \( Q_1 \) from \( Q_3 \):

$$ Q_3 - Q_1 = 12 - 6 = 6 $$

Answer:

6