Question

q3
b) find the iqr \\( q_3 - q_1 \\)
c) are there any outliers? \\( (q_1 - 1.5(iqr)) \\)
\\( (q_3 + 1.5(iqr)) \\)
6). a pack of m&ms contains the following: 6 red, 7 blue, 10 yellow, 3 orange, 5 green and 9 brown.
with this information, calculate the angles for a pie chart for the m&ms.
find relative frequency first
relative freg \\( \times 360 \\)

Explanation:

Step1: Calculate total number of M&Ms

First, sum up the number of each color: \( 6 + 7 + 10 + 3 + 5 + 9 \).
\( 6 + 7 = 13 \), \( 13 + 10 = 23 \), \( 23 + 3 = 26 \), \( 26 + 5 = 31 \), \( 31 + 9 = 40 \). So total \( n = 40 \).

Step2: Calculate relative frequency for each color

• Red: \( \frac{6}{40} = 0.15 \)
• Blue: \( \frac{7}{40} = 0.175 \)
• Yellow: \( \frac{10}{40} = 0.25 \)
• Orange: \( \frac{3}{40} = 0.075 \)
• Green: \( \frac{5}{40} = 0.125 \)
• Brown: \( \frac{9}{40} = 0.225 \)

Step3: Calculate pie chart angles (relative frequency × 360°)

• Red: \( 0.15 \times 360^\circ = 54^\circ \)
• Blue: \( 0.175 \times 360^\circ = 63^\circ \)
• Yellow: \( 0.25 \times 360^\circ = 90^\circ \)
• Orange: \( 0.075 \times 360^\circ = 27^\circ \)
• Green: \( 0.125 \times 360^\circ = 45^\circ \)
• Brown: \( 0.225 \times 360^\circ = 81^\circ \)

Answer:

• Red: \( 54^\circ \)
• Blue: \( 63^\circ \)
• Yellow: \( 90^\circ \)
• Orange: \( 27^\circ \)
• Green: \( 45^\circ \)
• Brown: \( 81^\circ \)