**How will Omar's mass increasing affect the mean and median?**:Mariah works at a zoo. She was looking at some data showing the masses of their
\[5\] African elephants. The mean mass of the elephants was
\[3{,}800\,{\text{kg}}\], and the median mass was
\[3{,}600\,{\text{kg}}\]. The heaviest elephant, named Omar, was recorded as
\[6{,}000\,{\text{kg}}\].
Mariah found out that Omar's mass was recorded incorrectly, and that Omar actually weighed
\[7{,}000\,{\text{kg}}\].
How will Omar's mass increasing affect the mean and median?
Choose 1 answer:
Choose 1 answer:
(Choice A)   Both the mean and median will increase.
A
Both the mean and median will increase.
(Choice B)   The mean will stay the same, and the median will increase.
B
The mean will stay the same, and the median will increase.
(Choice C)   The mean will increase, and the median will decrease.
C
The mean will increase, and the median will decrease.
(Choice D)   The mean will increase, and the median will stay the same.
D
The mean will increase, and the median will stay the same.

Let's analyze how increasing Omar's mass affects the mean and median.

### 1. **Effect on the Mean:**
The mean is calculated by summing all the masses and dividing by the number of elephants. Initially, the total mass of the 5 elephants is:
\[
\text{Total mass} = \text{Mean} \times \text{Number of elephants} = 3{,}800 \, \text{kg} \times 5 = 19{,}000 \, \text{kg}
\]
When Omar's mass is corrected from \(6{,}000 \, \text{kg}\) to \(7{,}000 \, \text{kg}\), the total mass becomes:
\[
\text{New total mass} = 19{,}000 \, \text{kg} + (7{,}000 \, \text{kg} - 6{,}000 \, \text{kg}) = 20{,}000 \, \text{kg}
\]
The new mean mass is:
\[
\text{New mean} = \frac{20{,}000 \, \text{kg}}{5} = 4{,}000 \, \text{kg}
\]
So, the mean increases.

### 2. **Effect on the Median:**
The median is the middle value when the masses are arranged in order. Increasing Omar's mass from \(6{,}000 \, \text{kg}\) to \(7{,}000 \, \text{kg}\) does not affect the order of the masses, and since the number of elephants is odd (5), the median remains the same as it is still the middle value.

### Conclusion:
- The **mean** will **increase** because the total mass increases.
- The **median** will **stay the same** because the middle value in the ordered list of masses does not change.

The correct answer is:
**(Choice D) The mean will increase, and the median will stay the same.**

Would you like any further details or explanations?

**Related questions:**
1. How is the mean affected if the lightest elephant's mass is decreased?
2. What happens to the median if two elephants have the same mass?
3. How would a new elephant being added to the zoo affect the mean and median?
4. How do outliers generally affect the mean and median?
5. What is the difference between the mean and median in a symmetric distribution?

**Tip:** 
When analyzing data sets, remember that the mean is sensitive to extreme values (outliers), while the median is more robust and less affected by outliers.

Understand how increasing the mass of an elephant affects the mean and median in a set of African elephants' data. Explore the calculation of mean and median, and how outliers influence these statistical measures. Suitable for Grades 6-8.

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