Reporting summary measures such as the mean, median, and standard deviation has become very common in modern life. Many companies, government agencies will report these descriptive measures of a variable, but they will rarely provide information on the shape of the distribution of that variable. In previous tutorials, you have learned some basic properties of some distributions that can help you to decide if a specific type of distribution is a good fit for a set of data. According to the National Diet and Nutrition Survey: Adults Aged 19 to 64, British men spend an average of 2.15 hours per day in moderate or high intensity physical activity. The standard deviation of these activity times for this sample was 3.59 hours. Can we infer that these activity times could follow a normal distribution? The following may provide an answer. Sketch a normal curve marking the points representing 1, 2, and 3 standard deviations above and below the mean, and calculate the values at these points using a mean of 2.15 hours and standard deviation of 3.59 hours. Examine the curve with your calculations. Explain why it is impossible for this distribution to be normal based on your graph and calculations. Considering the variable being measured, is it more likely that the distribution is skewed to the left or that it is skewed to the right? Explain why.
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.
Reporting summary measures such as the
According to the National Diet and Nutrition Survey: Adults Aged 19 to 64, British men spend an average of 2.15 hours per day in moderate or high intensity physical activity. The standard deviation of these activity times for this sample was 3.59 hours. Can we infer that these activity times could follow a
- Sketch a normal curve marking the points representing 1, 2, and 3 standard deviations above and below the mean, and calculate the values at these points using a mean of 2.15 hours and standard deviation of 3.59 hours.
- Examine the curve with your calculations. Explain why it is impossible for this distribution to be normal based on your graph and calculations.
- Considering the variable being measured, is it more likely that the distribution is skewed to the left or that it is skewed to the right? Explain why.
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