The ordered pairs below give the winning times (in seconds) of a 100-meter freestyle swim race at a regularly-held competition from 1984 through 2012. (1984, 55.12) (2000, 53.03) (1988, 54.13) (2004, 53.04) (1992, 53.84) (2008, 52.32) (1996, 53.70) (2012, 52.20) (a) Sketch a scatter plot of the data. Let y represent the winning time (in seconds) and let t = 84 represent 1984. (b) Sketch the line that you think best approximates the data and find an equation of the line. (Round the slope and y-intercept to one decimal place.) y = (c) Use the regression feature of a graphing utility to find the equation of the least squares regression line that fits the data. (Round the slope and y-intercept to two decimal places.) y =
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 ordered pairs below give the winning times (in seconds) of a 100-meter freestyle swim race at a regularly-held competition from 1984 through 2012.
| (1984, 55.12) | (2000, 53.03) | |
| (1988, 54.13) | (2004, 53.04) | |
| (1992, 53.84) | (2008, 52.32) | |
| (1996, 53.70) | (2012, 52.20) |
(b) Sketch the line that you think best approximates the data and find an equation of the line. (Round the slope and y-intercept to one decimal place.)
(c) Use the regression feature of a graphing utility to find the equation of the least squares regression line that fits the data. (Round the slope and y-intercept to two decimal places.)
(d) Compare the linear model you found in part (b) with the linear model you found in part (c).
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