Problem

4 These data sets include an outlier. Write down the outlier, then calculate the mean and the median. Include the outlier in your calculations.
$\begin{array}{lllllll}\text { a } & 5 & 7 & 7 & 8 & 12 & 33\end{array}$
$\begin{array}{llllll}\text { c } & -58 & -60 & -59 & -4 & -64\end{array}$
5 Decide if the following data sets are bimodal.
a $\begin{array}{lllllllll}2 & 7 & 9 & 5 & 6 & 2 & 8 & 7 & 4\end{array}$
b $1 \quad 6 \quad 2 \quad 3 \quad 3 \quad 1 \quad 5 \quad 4 \quad 1 \quad 9$
$\begin{array}{llllllllll}\text { d } & 23 & 25 & 26 & 23 & 19 & 24 & 28 & 26 & 27\end{array}$

Answer

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Answer

\(\boxed{\text{Dataset c: Outlier: -4, Mean: -49.0, Median: -59}}\)

Steps

Step 1 :First, let's identify the outliers in each dataset.

Step 2 :For dataset a: \(\begin{array}{lllllll} 5 & 7 & 7 & 8 & 12 & 33 \end{array}\), the outlier seems to be 33.

Step 3 :For dataset c: \(\begin{array}{llllll} -58 & -60 & -59 & -4 & -64 \end{array}\), the outlier seems to be -4.

Step 4 :Now, let's calculate the mean and median for each dataset.

Step 5 :Dataset a: Mean = \(\frac{5+7+7+8+12+33}{6} = 12.0\), Median = \(\frac{7+8}{2} = 7.5\)

Step 6 :Dataset c: Mean = \(\frac{-58+-60+-59+-4+-64}{5} = -49.0\), Median = -59

Step 7 :\(\boxed{\text{Dataset a: Outlier: 33, Mean: 12.0, Median: 7.5}}\)

Step 8 :\(\boxed{\text{Dataset c: Outlier: -4, Mean: -49.0, Median: -59}}\)

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