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Answer:
The Inter quartile range is $2.25.
Step-by-step explanation:
The Inter quartile range (<em>IQR</em>) is a quantity which tells amount of data contained between the first quartile (<em>Q</em>₁) and third quartile (<em>Q</em>₃).
The IQR can be computed using the formula:
The first quartile (<em>Q</em>₁) is well defined as the mid-value between the minimum value and the median of the data set. Or the mid-value of the first half of the data set is the first quartile.
The third quartile (<em>Q</em>₃) is the mid-value amid the median and the maximum value of the data set. Or the mid-value of the second half of the data set is the Third quartile.
The data set in arranged order is:
S = {$6.50, $8.75, $9.75, $10.25, $11.00, $12.75}
The first half of the data set is:
S₁ = {$6.50, $8.75, $9.75}
The mid-value is $8.75.
The first quartile is, <em>Q</em>₁ = $8.75.
The second half of the data set is:
S₁ = {$10.25, $11.00, $12.75}
The mid-value is $11.00.
The first quartile is, <em>Q</em>₃ = $11.00.
Compute the Inter quartile range as follows:
Thus, the Inter quartile range is $2.25.