Let's start by understanding the statistical measures involved: mean, median, and mode. These measures are often used to summarize a dataset.
1. The Mean:
The mean (or average) is calculated by summing all the values in the dataset and dividing by the number of values.
To calculate the mean for the given data:
[tex]\[
\text{Mean} = \frac{440 + 490 + 550 + 500 + 430 + 440 + 530 + 890}{8}
\][/tex]
Sum of the values:
[tex]\[
440 + 490 + 550 + 500 + 430 + 440 + 530 + 890 = 4270
\][/tex]
Number of values: 8
So, the mean is:
[tex]\[
\text{Mean} = \frac{4270}{8} = 533.75
\][/tex]
2. The Median:
The median is the middle value in a dataset when the values are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers.
First, arrange the values in ascending order:
[tex]\[
430, 440, 440, 490, 500, 530, 550, 890
\][/tex]
Since there are 8 values (an even number), the median will be the average of the 4th and 5th values:
[tex]\[
\text{Median} = \frac{490 + 500}{2} = 495
\][/tex]
3. The Mode:
The mode is the value that appears most frequently in a dataset.
In this dataset:
[tex]\[
430, 440, 440, 490, 500, 530, 550, 890
\][/tex]
The mode is:
[tex]\[
\text{Mode} = 440 \quad (\text{since 440 appears twice})
\][/tex]
Impact of the Highest Salary (890):
- The mean is calculated based on all values, so a very high (or low) value, such as 890, will significantly affect the mean.
- The median is the middle value and is less affected by extreme values since it depends only on the order of the data.
- The mode is the most frequent value and is not affected by the high value unless the extreme value is repeated more frequently than other values.
Therefore, the most affected measure by the highest salary (890) is:
[tex]\[
\boxed{\text{C) the mean}}
\][/tex]
