FREQUENCY DISTRIBUTIONS - Assignment Example

The average minutes that I use in physical fitness training, every day, is equal to 50.8. The figure is from data collected for duration of 10 days. The list number of minutes spent on physical fitness training is 38 minutes and the highest number of minutes is 60. The standard deviation is the square root of the variance. The standard deviation of the above data is 9.33 meaning that, on average, every value of the collected data is far from the mean by 9.33 units. Data falling within the range include 60,60,38,38,58,58,58,41,41,56, meaning that 100 percent of the sample is within the range.

For normally distributed data, only 5 percent of the value should fall outside the above range. Therefore, the above data is normally distributed. Additionally, the data does not have any outlets, which reflects the fact that it is normally distributed. A curve for a normally distributed data is bell shaped and symmetric, meaning that the data has an equal spread on both sides of the curve (William, 2003). The data is also continuous on both sides of the bell shape. Comparing normally distributed data and non-normal data, the estimates from normal data are more accurate compared to estimates from data that is not normally distributed (Bryc, 2013).

When defining normally distributed data, one must specify two quantities, including the mean (µ) and the standard deviation (σ).which reflects the spread of the curve. Different values of the mean and standard deviation yield different normal curves thus different normal distributions. Besides the 95 percent test, 99.7 percent test is also applicable while determining if data is normally distributed. 99.7 percent of all the values should fall within three standard deviations from the mean. In other words, they should fall between µ-3σ and µ+3σ (Berman, 2013).

More than 99.7% of the data fall within the range reflecting the fact that the data has a normal distribution. One of it implications