A population has µ=100 and õ=20. If you select a
single score from this population, on the average, how
close would it be to the population mean? Explain
your answer
It can only be stated in probability terms.
68% = within one SD
95% = within 2 SD
To determine how close a single score from a population would be to the population mean, we need to consider the concept of standard deviation.
In this case, the population mean is given as µ=100, and the population standard deviation is given as õ=20.
The standard deviation is a measure of how spread out the data is from the mean. A lower standard deviation indicates that the data points tend to be closer to the mean, while a higher standard deviation indicates greater variability.
In this example, the standard deviation is relatively high, which means there is more variability in the data points. Consequently, individual scores are likely to deviate more from the population mean compared to a population with a smaller standard deviation.
Therefore, if you select a single score from this population, on average it would be relatively far from the population mean of 100, due to the high standard deviation of 20. However, it is important to note that this is an average and does not guarantee the exact distance from the mean for any specific score.