12 young batsmen practiced batting at the nets for varying periods of time, and their dot ball percentage was calculated at the end of the month: Practice time per month (in hr) 43 30 55 12 28 37 41 48 34 18 24 62 Dot ball percentage 18 29 15 54 43 24 22 16 34 56 47 13 a) Find the relationship between dot ball percentage and practice time per month using a scatter diagram and interpret. b) Find correlation coefficient and comment. c) Fit a least square regression equation (line) of dot ball percentage on practice time per month and comment.
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.
12 young batsmen practiced batting at the nets for varying periods of time, and their dot ball percentage was calculated at the end of the month:
| Practice time per month (in hr) | 43 | 30 | 55 | 12 | 28 | 37 | 41 | 48 | 34 | 18 | 24 | 62 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Dot ball percentage | 18 | 29 | 15 | 54 | 43 | 24 | 22 | 16 | 34 | 56 | 47 | 13 |
a) Find the relationship between dot ball percentage and practice time per month using a
b) Find
c) Fit a least square regression equation (line) of dot ball percentage on practice time per month and comment.
d) What will be the dot ball percentage when practice time per month is 32hr?
e) Comment on the regression equation and explore how well it fits.
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