. A population has a mean of μ=35 and a standard deviation of σ=5. After 3 points are added to
every score in the population, calculate the new values for the mean and standard deviation?
μ has changed to μ+3
σ is unchanged
Adding 3 points to every score in the population is like giving everyone a participation trophy. It might boost their egos, but let's see how it affects the mean and standard deviation.
To find the new mean, we simply add 3 to the original mean. So the new mean would be 35 + 3 = 38. Now, let's move on to the standard deviation.
Adding a constant number to each data point doesn't change the shape or spread of the data. So, the standard deviation remains the same, which is σ = 5.
In conclusion, after adding 3 points to every score, the new mean becomes 38 and the standard deviation remains 5. I hope this clarification adds a little mathematical humor to your day!
To calculate the new values for the mean and standard deviation after adding 3 points to every score in the population, follow these steps:
Step 1: Calculate the new mean:
The new mean (μ') can be found by adding 3 to the original mean (μ).
μ' = μ + 3
Given that μ = 35, substituting this value into the equation:
μ' = 35 + 3
μ' = 38
So, the new mean is 38.
Step 2: Calculate the new standard deviation:
The new standard deviation (σ') can be found by using the formula:
σ' = σ
Given that σ = 5, the new standard deviation remains the same.
So, the new standard deviation is also 5.
Therefore, the new values for the mean and standard deviation are μ' = 38 and σ' = 5, respectively.
To calculate the new values for the mean and standard deviation after adding 3 points to every score in the population, follow these steps:
1. Find the new mean:
The new mean can be calculated by adding 3 to the original mean. In this case, the original mean is μ=35, so the new mean will be:
New mean = Original mean + 3
= 35 + 3
= 38
2. Find the new standard deviation:
The new standard deviation remains the same, as adding a constant value to each score does not affect the spread or variability of the data. Therefore, the new standard deviation will still be:
New standard deviation = Original standard deviation
= σ
= 5
So, the new values for the mean and standard deviation will be:
New mean = 38
New standard deviation = 5