A population has a mean of � � 30 and a standard
deviation of � � 5.
a. If 5 points were added to every score in the
population, what would be the new values for the
mean and standard deviation?
b. If every score in the population were multiplied by
3 what would be the new values for the mean and
standard deviation?
a. mean = 35; standard deviation of 5 stays the same.
b. mean = 90; standard deviation = 15
A distribution has a standard deviation of � � 12.
Find the z-score for each of the following locations
in the distribution.
a. Above the mean by 3 points.
b. Above the mean by 12 points.
c. Below the mean by 24 points.
d. Below the mean by 18 points.
For the following population of N � 6 scores:
3, 1, 4, 3, 3, 4
a. Sketch a histogram showing the population
distribution.
b. Locate the value of the population mean in your
sketch, and make an estimate of the standard
deviation (as done in Example 4.2).
c. Compute SS, variance, and standard deviation for
the population. (How well does your estimate
compare with the actual value of �?)
In a population of exam scores, a score of X � 48
corresponds to z��1.00 and a score of X � 36
corresponds to z � –0.50. Find the mean and standard
deviation for the population. (Hint: Sketch the
distribution and locate the two scores on your sketch.)
A sample consists of the following n � 6 scores: 2, 7,
4, 6, 4, and 7.
a. Compute the mean and standard deviation for the
sample.
b. Find the z-score for each score in the sample.
c. Transform the original sample into a new sample
with a mean of M � 50 and s � 10.
bb
a. If 5 points were added to every score in the population, the mean would also increase by 5. So the new mean would be 35. However, the standard deviation would remain unchanged at 5. Adding a constant value does not affect the spread of the data.
b. If every score in the population were multiplied by 3, the mean would also be multiplied by 3, so the new mean would be 90. The standard deviation would also be multiplied by 3, resulting in a new standard deviation of 15. Multiplying the data points by a constant increases both the mean and the spread of the data. It's like giving everyone "growth hormones", things get bigger and more spread out.
To find the new mean and standard deviation after performing certain operations on a population, you can use the following formulas:
For adding a constant value to every score:
New Mean = Old Mean + Constant Value
New Standard Deviation remains the same.
For multiplying every score by a constant value:
New Mean = Old Mean multiplied by the Constant Value
New Standard Deviation = Old Standard Deviation multiplied by the Absolute Value of the Constant Value
Now, let's calculate the new values for each scenario:
a. If 5 points were added to every score in the population:
New Mean = 30 + 5 = 35
New Standard Deviation remains the same at 5.
b. If every score in the population were multiplied by 3:
New Mean = 30 * 3 = 90
New Standard Deviation = 5 * 3 = 15
Therefore, the new values are:
a. New Mean = 35, New Standard Deviation = 5
b. New Mean = 90, New Standard Deviation = 15