The following 10 scores were input in the gradebook for Prof. Torres's class. $$ 17,73,75,84,84,88,89,93,94,190 $$ 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".

Question

UpStudy AI · Accepted Answer

We start with the 10 scores arranged in increasing order:
$$
17,\ 73,\ 75,\ 84,\ 84,\ 88,\ 89,\ 93,\ 94,\ 190
$$

**Step 1. Find $$ Q_1 $$ and $$ Q_3 $$:**

Since there are 10 scores, divide the data into a lower half and an upper half.

Lower half (first 5 scores):
$$
17,\,73,\,75,\,84,\,84
$$
The median of these 5 values is the third value:
$$
Q_1 = 75
$$

Upper half (last 5 scores):
$$
88,\,89,\,93,\,94,\,190
$$
The median of these values is the third value:
$$
Q_3 = 93
$$

**Step 2. Calculate the Interquartile Range (IQR):**

$$
\text{IQR} = Q_3 - Q_1 = 93 - 75 = 18
$$

**Step 3. Determine the outlier boundaries:**

Lower boundary:
$$
Q_1 - 1.5 \times \text{IQR} = 75 - 1.5(18) = 75 - 27 = 48
$$

Upper boundary:
$$
Q_3 + 1.5 \times \text{IQR} = 93 + 1.5(18) = 93 + 27 = 120
$$

**Step 4. Identify the outliers:**

Any score less than $$ 48 $$ or greater than $$ 120 $$ is an outlier.

Checking the scores:
- $$ 17 < 48 $$ so $$ 17 $$ is an outlier.
- $$ 190 > 120 $$ so $$ 190 $$ is an outlier.

Thus, the outliers are:
$$
17, 190
$$
The outliers are 17 and 190.

The following 10 scores were input in the gradebook for Prof. Torres's class. \[ 17,73,75,84,84,88,89,93,94,190 \] 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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