Question

Select the outlier in the data set.
If the outlier were removed from the data set, would the mean increase or decrease?


19 72 24 93 20 28 834 99 75 81 95 83 50 21 97 61

Answer 1

To identify the outlier in the data set, let's first look at the numbers provided:

19, 72, 24, 93, 20, 28, 834, 99, 75, 81, 95, 83, 50, 21, 97, 61

It is evident that "834" is significantly larger than the other numbers in the data set. All the others are relatively small compared to 834. Therefore, 834 is the outlier.

Now, if we remove the outlier (834) from the data set, we should assess the effect on the mean. The mean is the average of all values in the data set.

Let's calculate the mean of the data set:

1. **Sum of the data set:**
\( 19 + 72 + 24 + 93 + 20 + 28 + 834 + 99 + 75 + 81 + 95 + 83 + 50 + 21 + 97 + 61 = 1094 \)

2. **Count of the data set:**
There are 16 numbers in total.

3. **Mean with the outlier:**
\[
\text{Mean} = \frac{1094}{16} = 68.375
\]

Now, let's remove the outlier (834):

1. **New sum of the remaining data:**
\( 19 + 72 + 24 + 93 + 20 + 28 + 99 + 75 + 81 + 95 + 83 + 50 + 21 + 97 + 61 = 703 \)

2. **New count of data:**
There are now 15 numbers.

3. **Mean without the outlier:**
\[
\text{Mean} = \frac{703}{15} = 46.867
\]

### Conclusion:
- The outlier is **834**.
- Removing the outlier would cause the mean to **decrease** from approximately 68.375 to approximately 46.867.