Questions: The data show the number of hours of television watched per day by a sample of 11 people 991578103649 a. Obtain the quartiles. b. Determine the interquartile range (IQR) c. Find the five-number summary

Solution Steps

First, we sort the given data to facilitate the calculation of quartiles and the five-number summary. The sorted data is: \[ [1, 3, 4, 5, 6, 7, 8, 9, 9, 9, 10] \]

To find the quartiles, we use the formula for the rank of the quantile: \[ \text{Rank} = Q \times (N + 1) \] where \( Q \) is the quantile value and \( N \) is the number of data points.

• First Quartile (\(Q_1\)): \[ \text{Rank} = 0.25 \times (11 + 1) = 3.0 \] The value at position 3 is 4. Thus, \( Q_1 = 4 \).

• Second Quartile (\(Q_2\)) or Median: \[ \text{Rank} = 0.5 \times (11 + 1) = 6.0 \] The value at position 6 is 7. Thus, \( Q_2 = 7 \).

• Third Quartile (\(Q_3\)): \[ \text{Rank} = 0.75 \times (11 + 1) = 9.0 \] The value at position 9 is 9. Thus, \( Q_3 = 9 \).

The interquartile range is calculated as: \[ \text{IQR} = Q_3 - Q_1 = 9 - 4 = 5 \]

The five-number summary consists of the minimum, first quartile, median, third quartile, and maximum values:

• Minimum: 1
• First Quartile (\(Q_1\)): 4
• Median (\(Q_2\)): 7
• Third Quartile (\(Q_3\)): 9
• Maximum: 10

Thus, the five-number summary is: \[ [1, 4, 7, 9, 10] \]

Final Answer