The 11 members of the swim team completed the following numbers of laps at today's practice. $$ 76,76,78,80,81,82,83,84,85,87,90 $$ Identify all values that are outliers. If there is more than one outlier, separate them with commas. If there are no outliers, click on "None".

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We first identify the median ( $$Q_2$$ ), first quartile ( $$Q_1$$ ), and third quartile ( $$Q_3$$ ) of the dataset. The data in sorted order is:

$$
76,\; 76,\; 78,\; 80,\; 81,\; 82,\; 83,\; 84,\; 85,\; 87,\; 90
$$

Since there are 11 data points, the median is the $$6^{\text{th}}$$ term:

$$
Q_2 = 82
$$

The lower half (not including the median) is:

$$
76,\; 76,\; 78,\; 80,\; 81
$$

So, the first quartile is the median of these $$5$$ values:

$$
Q_1 = 78
$$

The upper half (not including the median) is:

$$
83,\; 84,\; 85,\; 87,\; 90
$$

So, the third quartile is the median of these $$5$$ values:

$$
Q_3 = 85
$$

The interquartile range (IQR) is:

$$
\text{IQR} = Q_3 - Q_1 = 85 - 78 = 7
$$

Next, we calculate the fences for outliers. An observation is an outlier if it is below:

$$
Q_1 - 1.5 \times \text{IQR} = 78 - 1.5 \times 7 = 78 - 10.5 = 67.5
$$

or above:

$$
Q_3 + 1.5 \times \text{IQR} = 85 + 1.5 \times 7 = 85 + 10.5 = 95.5
$$

Now, we check the dataset: all values lie between $$67.5$$ and $$95.5$$. Therefore, there are no outliers.

None
There are no outliers.

The 11 members of the swim team completed the following numbers of laps at today's practice. \[ 76,76,78,80,81,82,83,84,85,87,90 \] Identify all values that are outliers. If there is more than one outlier, separate them with commas. If there are no outliers, click on "None".

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