This is a standard deviation question.
I don't know much about standard deviation.
Here it goes... Teachers making 30,000 to $60,000 the union is considering a $1,000 pay raise.
A. Will the standard deviation change and the mean and the median stay the same?
B. Will the mean and the median change and the same and the standard deviation stay the same?
c. will the median and standard deviation change and mean stay the same?
D. will the mean and standard deviation change and the median stay the same?
I think B, but the language is garbled.
The SD will not change. Read up on how the SD is figured, and you should see why.
To answer this question, we need to understand the concept of standard deviation and how it relates to the given scenario.
Standard deviation is a measure of the dispersion or spread of a set of values. It tells us how much the individual values differ from the mean (average) value of the dataset.
In this scenario, the teachers' salaries range from $30,000 to $60,000, with the union considering a $1,000 pay raise.
Now let's analyze each option:
A. Will the standard deviation change and the mean and the median stay the same?
When a fixed amount, such as a pay raise, is added to or subtracted from each value in a dataset, the standard deviation remains the same. The mean (average) and median will both increase by the same amount as the pay raise. Therefore, Option A is incorrect.
B. Will the mean and the median change and the same and the standard deviation stay the same?
As mentioned earlier, when a fixed amount is added to or subtracted from each value in a dataset, the mean and median will both increase by the same amount. However, the standard deviation will remain unchanged. So, Option B is correct.
C. Will the median and standard deviation change and mean stay the same?
In this scenario, the pay raise only affects the mean and median values, not the dispersion or spread of data. Therefore, the standard deviation will remain the same. Option C is not correct.
D. Will the mean and standard deviation change and the median stay the same?
As mentioned previously, the mean will increase by the same amount as the pay raise. However, the standard deviation is not affected by the addition or subtraction of a fixed amount. The median will also increase by the same amount as the pay raise. Therefore, Option D is incorrect.
To summarize, the correct answer is Option B: the mean and median will change by the amount of the pay raise, while the standard deviation will stay the same.