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 51 53 65 54 51 75 56 59 61 73 71 31 47 45 41 37 65 70 60 47 31 76 55 65 42 25 69 78 78 53 27 41 41 29 Ages of Best Male Actor Award Recipients 50 59 64 72 71 76 73 43 32 32 43 34 64 47 45 31 46 48 57 57 59 66 64 68 64 61 30 71 55 43 74 65 73 69 (a) Find the mean and the sample standard deviation of the ages of the female recipients. Round each result to the nearest tenth. mean yr sample standard deviation yr (b) Find the mean and the sample standard deviation of the ages of the male recipients. Round each result to the nearest tenth. mean yr sample standard deviation yr (c) Which of the two data sets has the larger mean? female actors male actors Which of the two data sets has the larger standard deviation? female actors 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.)
| 51 53 65 54 51 75 56 59 61 73 71 31 47 45 41 37 65 70 60 47 31 76 55 65 42 25 69 78 78 53 27 41 41 29 |
| 50 59 64 72 71 76 73 43 32 32 43 34 64 47 45 31 46 48 57 57 59 66 64 68 64 61 30 71 55 43 74 65 73 69 |
| mean | yr |
| sample standard deviation | yr |
(b) Find the mean and the sample standard deviation of the ages of the male recipients. Round each result to the nearest tenth.
| mean | yr |
| sample standard deviation | yr |
(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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