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If data set \(T =\{1, 8, 0, z, -2\}\), what is the value of \(z\) ?
(1) The range of data set \(T\) is 12
(2) The average (arithmetic mean) of data set \(T\) is \(\frac{3}{5}\)
(1) The range of data set \(T\) is 12
(2) The average (arithmetic mean) of data set \(T\) is \(\frac{3}{5}\)
16 Sep 2014, 01:17
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Official Solution:
If data set \(T =\{1, 8, 0, z, -2\}\), what is the value of \(z\) ?
(1) The range of data set \(T\) is 12
When considering the range of \(T =\{1, 8, 0, z, -2\}\) without \(z\), the difference between the largest and smallest elements is 8 - (-2) = 10. Given that the range of \(T\) is 12, \(z\) must be either the largest or the smallest element. If \(z\) is the largest element, then \(z - (-2) = 12\), implying that \(z = 10\). If \(z\) is the smallest element, then \(8 - z = 12\), implying that \(z = -4\). Not sufficient.
(2) The average (arithmetic mean) of data set \(T\) is \(\frac{3}{5}\)
The average is calculated as \(\frac{1 + 8 + 0 + z - 2}{5} = \frac{3}{5}\). From this, we deduce that \(z = -4\). Sufficient.
Answer: B
If data set \(T =\{1, 8, 0, z, -2\}\), what is the value of \(z\) ?
(1) The range of data set \(T\) is 12
When considering the range of \(T =\{1, 8, 0, z, -2\}\) without \(z\), the difference between the largest and smallest elements is 8 - (-2) = 10. Given that the range of \(T\) is 12, \(z\) must be either the largest or the smallest element. If \(z\) is the largest element, then \(z - (-2) = 12\), implying that \(z = 10\). If \(z\) is the smallest element, then \(8 - z = 12\), implying that \(z = -4\). Not sufficient.
(2) The average (arithmetic mean) of data set \(T\) is \(\frac{3}{5}\)
The average is calculated as \(\frac{1 + 8 + 0 + z - 2}{5} = \frac{3}{5}\). From this, we deduce that \(z = -4\). Sufficient.
Answer: B
22 Oct 2023, 03:05
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I've revised the question and solution, incorporating additional details for improved clarity. I trust this makes it more comprehensible.
