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Sia

Question
Math
Posted 6 months ago

The stem and leaf plot shows the number of days of snowfall at a winter sports resort for each of the past 17 years.
\begin{tabular}{c|llllllllll} 
stem & leaf & & & & & & & \\
\hline 5 & 0 & 7 & & & & & & & \\
6 & 2 & 4 & 5 & 5 & 5 & 8 & & & \\
7 & 0 & 1 & 2 & 2 & 3 & 4 & 7 & 9 & 9
\end{tabular}

Key: 626 \mid 2 represents a year with 62 days of snowfall.
Here is the five-number summary for these data:
Five-number summary
\begin{tabular}{ccccc}
min\min & Q1\mathrm{Q}_{1} & median & Q3\mathrm{Q}_{3} & max\max \\
\hline 50 & 64.5 & 70 & 73.5 & 79
\end{tabular}

According to the 1.5IQR1.5 \cdot \mathrm{IQR} rule for outliers, how many high outliers are there in the data set?

Choose 1 answer:
(A) 0
(B) 1\mathbf{1}
(C) 2
(D) 3
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Answer from Sia
Posted 6 months ago
Solution by Steps
step 1
Calculate the interquartile range (IQR) by subtracting the first quartile (Q1Q_1) from the third quartile (Q3Q_3)
step 2
IQR=Q3Q1=73.564.5=9IQR = Q_3 - Q_1 = 73.5 - 64.5 = 9
step 3
Determine the threshold for high outliers by adding 1.5IQR1.5 \cdot IQR to the third quartile (Q3Q_3)
step 4
High outlier threshold = Q3+1.5IQR=73.5+1.59=73.5+13.5=87Q_3 + 1.5 \cdot IQR = 73.5 + 1.5 \cdot 9 = 73.5 + 13.5 = 87
step 5
Identify the number of data points exceeding the high outlier threshold. According to the stem-and-leaf plot, there are no data points above 87, so there are no high outliers
Answer
(A) 0
Key Concept
1.5 IQR Rule for Outliers
Explanation
The 1.5 IQR rule is used to identify outliers by creating a threshold above or below which data points are considered outliers. In this case, no data points exceed the high outlier threshold, so there are no high outliers.

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