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: $6 \mid 2$ represents a year with 62 days of snowfall.
Here is the five-number summary for these data:
Five-number summary
\begin{tabular}{ccccc}
$\min$ & $\mathrm{Q}_{1}$ & median & $\mathrm{Q}_{3}$ & $\max$ \\
\hline 50 & 64.5 & 70 & 73.5 & 79
\end{tabular}
According to the $1.5 \cdot \mathrm{IQR}$ rule for outliers, how many high outliers are there in the data set?
Choose 1 answer:
(A) 0
(B) $\mathbf{1}$
(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 ($Q_1$) from the third quartile ($Q_3$)

step 2

$IQR = Q_3 - Q_1 = 73.5 - 64.5 = 9$

step 3

Determine the threshold for high outliers by adding $1.5 \cdot IQR$ to the third quartile ($Q_3$)

step 4

High outlier threshold = $Q_3 + 1.5 \cdot IQR = 73.5 + 1.5 \cdot 9 = 73.5 + 13.5 = 87$

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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