Question
Students were asked how much money they had in their pocket. The results are as follows: \( \begin{array}{llllllllllllllll}0 & 0 & 1 & 3 & 3 & 5 & 5 & 5 & 6 & 7 & 9 & 10 & 10 & 13 & 20 & 20 \\ 22 & 23 & 25 & 31 & 95\end{array} \) The 5 number summary and IQR have been calculated for you. Q1:4 Min: 0 IQR: 17 Max:95 Median:9 Leave your answers as decimals if needed. Don't 21 round. The low end value is The high end value is
Ask by Willis Young. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The low end value is -21.5 and the high end value is 46.5.
Solution
The low end value is calculated using the formula
\[
\text{Low end} = Q_1 - 1.5 \times IQR.
\]
Substitute the given values:
\[
\text{Low end} = 4 - 1.5 \times 17 = 4 - 25.5 = -21.5.
\]
The high end value is calculated using the formula
\[
\text{High end} = Q_3 + 1.5 \times IQR.
\]
Since
\[
IQR = Q_3 - Q_1 \quad \Longrightarrow \quad Q_3 = Q_1 + IQR = 4 + 17 = 21,
\]
we have
\[
\text{High end} = 21 + 1.5 \times 17 = 21 + 25.5 = 46.5.
\]
Thus, the low end value is \(-21.5\) and the high end value is \(46.5\).
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Simplify this solution Extra Insights
The low-end value, also known as the lower bound for potential outliers, can be found using the formula: \(Q1 - 1.5 \times IQR\). Plugging in the values, we have \(4 - 1.5 \times 17 = 4 - 25.5 = -21.5\). Since we can't have a negative amount of money, the low-end value would be considered as 0. For the high-end value, we use the formula: \(Q3 + 1.5 \times IQR\). Here, \(Q3\) is calculated as \(Q1 + IQR\), which gives us \(4 + 17 = 21\). Therefore, the high-end value is \(21 + 1.5 \times 17 = 21 + 25.5 = 46.5\). Thus, the high-end value is 46.5.
