A dataset includes the following values: 45, 47, 50, 52, 60. If a mistake is found and the value 60 should have been 50, what is the impact on the mean and median?

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1 point

a. Mean decreases, median increases.

b. Mean stays the same, median decreases.

c. Mean decreases, median stays the same.

d. Mean and median both will decrease.

Let's analyze how changing the value from 60 to 50 affects both the mean and median.

**Original dataset**: 45, 47, 50, 52, 60  
**Corrected dataset** (with 60 replaced by 50): 45, 47, 50, 50, 52

### Step 1: Calculating the mean

The **mean** is the sum of the values divided by the number of values.

- Original dataset:
  \[
  \text{Mean} = \frac{45 + 47 + 50 + 52 + 60}{5} = \frac{254}{5} = 50.8
  \]

- Corrected dataset:
  \[
  \text{Mean} = \frac{45 + 47 + 50 + 50 + 52}{5} = \frac{244}{5} = 48.8
  \]

The **mean decreases** from 50.8 to 48.8.

### Step 2: Calculating the median

The **median** is the middle value when the data is arranged in order.

- Original dataset: 45, 47, 50, 52, 60 → Median = 50 (middle value)
- Corrected dataset: 45, 47, 50, 50, 52 → Median = 50 (middle value)

The **median stays the same** at 50.

### Conclusion:
The **mean decreases**, and the **median stays the same**. Therefore, the correct answer is:

**c. Mean decreases, median stays the same.**

Would you like further details on any of the steps?

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Here are 5 related questions you might find helpful:
1. What is the impact of an outlier on the mean and median?
2. How do you calculate the median for an even set of numbers?
3. How does replacing a value in a dataset typically affect the mode?
4. What happens to the mean and median when all values in a dataset are increased by a constant?
5. Can the mean and median be equal in any dataset?

**Tip**: The median is more resistant to outliers than the mean, which is why small data modifications often don't change the median as much.

A dataset includes the following values: 45, 47, 50, 52, 60. If a mistake is found and the value 60 should have been 50, what is the impact on the mean and median?

Explore how replacing a value in a dataset affects the mean and median. Given the dataset 45, 47, 50, 52, 60, learn how a change from 60 to 50 decreases the mean but keeps the median unchanged. Suitable for students in Grades 6-8.

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