A student asks, "If the average income of 10 people is $10,000 and one person gets a raise of $10,000, is the median, the mean, or the mode changed and, if so, by how much?"

now way to tell about the median and mode, but the mean is changed from

(10*10000)/10 to (9*10000+20000)/10

To determine how the median, mean, and mode are affected when one person gets a raise of $10,000, let's analyze each measure one by one.

1. Mean: The mean is the average value of a set of numbers. To calculate the mean, we add up all the numbers and divide by the total count.

Since the average income of 10 people is $10,000, the total income of all 10 people would be $10,000 x 10 = $100,000.

Now, when one person gets a raise of $10,000, the new total income would be $100,000 + $10,000 = $110,000.

The new mean would be the new total income divided by the total count of people, which is $110,000 / 10 = $11,000.

Therefore, the mean has changed from $10,000 to $11,000, an increase of $1,000.

2. Median: The median is the middle value in a sorted list of numbers. Since we don't have a specific list of numbers, we can't determine the median.

For example, if the original incomes were: $8,000, $9,000, $10,000, $10,000, $10,000, $10,000, $10,000, $10,000, $10,000, and $12,000, the median would be $10,000. However, without specific values, we can't determine the new median.

3. Mode: The mode is the value(s) that appear most frequently in a set of numbers. Since we don't have specific values, we can't determine the mode either.

In conclusion, based on the given information, we can only say that the mean has changed from $10,000 to $11,000 with an increase of $1,000. The effect on the median and the mode cannot be determined without knowing the specific incomes before and after the raise.

To determine whether the median, mean, or mode is affected by the given scenario, we need to understand what each of these terms represents.

1. Mean: The mean is also known as the average. To calculate it, we add up all the values and divide by the total number of values.

2. Median: The median is the middle value when the data is arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values.

3. Mode: The mode is the value that appears most frequently in the dataset. If no value repeats, there is no mode.

Now, let's analyze the scenario. Initially, the average income of 10 people is $10,000, which means the sum of all the incomes is 10 * $10,000 = $100,000.

If one person gets a raise of $10,000, their income becomes $10,000 + $10,000 = $20,000.

To assess the impact on the measures of central tendency:
- Mean: Since the mean is affected by extreme values, the sum of the incomes remains the same ($100,000 + $10,000 = $110,000), but now divided by 10 people. Therefore, the new mean is $110,000 / 10 = $11,000. The mean has increased by $1,000.

- Median: The median is unaffected by changes in extreme values or by the upper and lower extremes. As only one person's income changed, the position of the median remains the same, and it remains unchanged at $10,000.

- Mode: The mode is unaffected because it represents the most frequently occurring value. As no other person experienced a raise or change in their income, the mode remains unchanged.

So, in summary, the median and mode are unaffected by the given scenario, whereas the mean has increased by $1,000.