Questions: Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers.

Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers.
Transcript text: Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers.
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Solution

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Solution Steps

Step 1: Calculate the First Quartile (\(Q_1\))

To find the first quartile (\(Q_1\)), we use the formula for the rank: \[ \text{Rank} = Q \times (N + 1) \] where \( Q = 0.25 \) and \( N = 15 \) (the number of data points).

\[ \text{Rank} = 0.25 \times (15 + 1) = 0.25 \times 16 = 4.0 \]

The quantile is at position 4 in the sorted data, which corresponds to the value 10.

Thus, the first quartile, \(Q_1\), is: \[ \boxed{10} \]

Step 2: Calculate the Second Quartile (\(Q_2\))

To find the second quartile (\(Q_2\)), which is the median, we use the same formula for the rank: \[ \text{Rank} = Q \times (N + 1) \] where \( Q = 0.5 \).

\[ \text{Rank} = 0.5 \times (15 + 1) = 0.5 \times 16 = 8.0 \]

The quantile is at position 8 in the sorted data, which corresponds to the value 14.

Thus, the second quartile, \(Q_2\), is: \[ \boxed{14} \]

Step 3: Calculate the Third Quartile (\(Q_3\))

To find the third quartile (\(Q_3\)), we use the same formula for the rank: \[ \text{Rank} = Q \times (N + 1) \] where \( Q = 0.75 \).

\[ \text{Rank} = 0.75 \times (15 + 1) = 0.75 \times 16 = 12.0 \]

The quantile is at position 12 in the sorted data, which corresponds to the value 20.

Thus, the third quartile, \(Q_3\), is: \[ \boxed{20} \]

Final Answer

  • The first quartile, \(Q_1\), is \( \boxed{10} \).
  • The second quartile, \(Q_2\), is \( \boxed{14} \).
  • The third quartile, \(Q_3\), is \( \boxed{20} \).
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