Question

1. a population has a mean of μ = 50 and a standard deviation of σ = 10. a. if 3 points were added to every score in the popula - tion, what would be the new values for the mean and standard deviation? b. if every score in the population were multiplied by 2, then what would be the new values for the mean and standard deviation?

Explanation:

Step1: Recall the effect of adding a constant to data

When a constant \(c\) is added to each data - point in a population, the mean changes by the same constant, and the standard deviation remains the same. Here \(c = 3\), \(\mu=50\) and \(\sigma = 10\).
The new mean \(\mu_{new}=\mu + c=50 + 3=53\), and the new standard deviation \(\sigma_{new}=\sigma = 10\).

Step2: Recall the effect of multiplying data by a constant

When each data - point in a population is multiplied by a constant \(k\), the mean is multiplied by \(k\) and the standard deviation is also multiplied by \(k\). Here \(k = 2\), \(\mu = 50\) and \(\sigma=10\).
The new mean \(\mu_{new}=k\mu=2\times50 = 100\), and the new standard deviation \(\sigma_{new}=k\sigma=2\times10 = 20\).

Answer:

a. Mean = 53, Standard deviation = 10
b. Mean = 100, Standard deviation = 20