The following tables list the ages of female and male actors when they starred in their award-winning Best Actor performances. (A graphing calculator is recommended.) Ages of Best Female Actor Award Recipients 57 76 28 43 54 33 36 42 66 67 60 26 37 62 43 55 73 58 35 44 68 61 27 69 59 34 75 32 74 56 67 33 55 21 Ages of Best Male Actor Award Recipients 45 54 45 61 60 35 43 34 31 68 65 47 30 66 61 33 42 35 51 60 34 42 33 58 72 74 46 36 39 37 48 61 40 76 (a) Find the mean and the sample standard deviation of the ages of the female recipients. Round each result to the nearest tenth. mean sample standard deviation (b) Find the mean and the sample standard deviation of the ages of the male recipients. Round each result to the nearest tenth. mean sample deviation (c) Which of the two data sets has the larger mean? female actors or male actors Which of the two data sets has the larger standard deviation? female actors or male actors
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The following tables list the ages of female and male actors when they starred in their award-winning Best Actor performances. (A graphing calculator is recommended.)
| 57 76 28 43 54 33 36 42 66 67 60 26 37 62 43 55 73 58 35 44 68 61 27 69 59 34 75 32 74 56 67 33 55 21 |
| 45 54 45 61 60 35 43 34 31 68 65 47 30 66 61 33 42 35 51 60 34 42 33 58 72 74 46 36 39 37 48 61 40 76 |
(b) Find the mean and the sample standard deviation of the ages of the male recipients. Round each result to the nearest tenth.
(c) Which of the two data sets has the larger mean?
Which of the two data sets has the larger standard deviation?
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