lity? Let x be random variable representing the price (in dollars) of a shoe, while y represents the quality rating (on a scale of 0 to 100). The following table shows data from Consumer Reports for six different brands of men’s athletic shoes. x 80 45 30 80 110 70 y 52 62 56 58 51 51 a) Plot a scatter diagram of the data. (Draw an accurate graph, on graph paper if possible. Make sure to write labels, and choose a consistent scale, equally spaced apart, on each axis.) b) Based on the scatterplot, would you estimate the correlation coefficient to be positive, close to zero, or negative? c) Interpret your results from parts (a) and (b).
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.
Is the price of a men’s athletic shoe related to the quality? Let x be random variable representing the price (in dollars) of a shoe, while y represents the quality rating (on a scale of 0 to 100). The following table shows data from Consumer Reports for six different brands of men’s athletic shoes.
x 80 45 30 80 110 70 y 52 62 56 58 51 51
-
a) Plot a
scatter diagram of the data.
(Draw an accurate graph, on graph paper if possible. Make sure to write labels, and choose a consistent scale, equally spaced apart, on each axis.) -
b) Based on the scatterplot, would you estimate the
correlation coefficient to be positive, close to zero, or negative? -
c) Interpret your results from parts (a) and (b).
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