If the score of 33 is removed from the data set below, which of these statements is not true?
12, 15, 12, 17, 19, 25, 15, 11, 13, 18, 12, 16, 12, 19, 33, 20
(1 Point)

The mode is unchanged

The mean and median are both reduced in value

The range is smaller

The measures of centre are unchanged

Let's analyze the impact of removing the score of 33 from the given data set:

### Original Data Set:
12, 15, 12, 17, 19, 25, 15, 11, 13, 18, 12, 16, 12, 19, 33, 20

### After Removing 33:
12, 15, 12, 17, 19, 25, 15, 11, 13, 18, 12, 16, 12, 19, 20

Now, let's consider each statement:

1. **The mode is unchanged:**
   - The mode is the number that appears most frequently in the data set.
   - Before removing 33: The mode is 12 (which appears 4 times).
   - After removing 33: The mode is still 12.
   - **This statement is true.**

2. **The mean and median are both reduced in value:**
   - The mean is the average of the data set.
   - The median is the middle value when the data set is ordered.
   - Removing 33 (a relatively high number) would generally reduce the mean.
   - The median might also be affected, depending on the data set.
   - **This statement is true.**

3. **The range is smaller:**
   - The range is the difference between the highest and lowest values.
   - Original range: \( 33 - 11 = 22 \).
   - After removing 33, the new highest value is 25.
   - New range: \( 25 - 11 = 14 \).
   - **This statement is true.**

4. **The measures of center are unchanged:**
   - The measures of center (mean and median) would be affected by the removal of 33.
   - **This statement is not true.**

### Conclusion:
The statement **"The measures of center are unchanged"** is not true.

Would you like to know more details or have any questions? Here are some related questions to explore:

1. How do you calculate the mean of a data set?
2. What is the significance of the mode in a data set?
3. How does removing an outlier affect the median?
4. Why is the range important in understanding data dispersion?
5. What happens to the variance when you remove a high-value outlier from a data set?

**Tip:** Removing outliers can significantly impact the measures of central tendency and spread in a data set, such as the mean, median, and range.

Explore how removing an outlier affects statistical measures like mean, median, mode, and range in a data set. Understand why outliers can significantly alter these measures. Detailed analysis and examples provided.

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