By Mohammed A. Shayib

Utilized facts has come into lifestyles as an final result of an scan and large adventure of greater than forty years. utilized statistics is meant to introduce the recommendations, definitions, and terminology of the topic in an hassle-free presentation with minimal mathematical historical past which doesn't surpass collage algebra. utilized facts may still arrange the reader to make a great determination according to facts. the fabric, contained in utilized facts, might be lined in a 15-week, 3-hours-per-week semester, with little adjustment as time permits.

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In such a case it is not easy to find an exact value for the mean or the standard deviation. Given the frequency table for the data, we will assume that within each class the mean of the data values, in that class, is equal to the class midpoint. We then multiply the class midpoint by the frequency of that class. This product is expected to be very close to the sum of the data that lie in that class. The process is repeated for all the classes, and the total will be calculated. This sum approximates the total of the data on hand.

38 Applied Statistics Descriptive Statistics Our discussion Starts with the mean of the population μ, and how those observations are distributed around that value of μ. We are interested in the variability of the observations, in other words, we like to see what variation is there by calculating the variance and the standard deviation by using μ as a reference point. e. in the difference Yi – μ. This difference is called the deviation of the observation Yi from the mean μ. Based on the definition of the mean for a finite population, it is easily seen that “the sum of the deviations of all data points from the mean of the finite population” is zero.

E. there are no units of measurement for the Z-score. There are two Z-scores, a Z-score for the population and another one for the sample. Their formulas are respectively given by Population Z- Score: Z = Sample Z- score: Z= x−µ σ (Y – Y) S The Z-score has mean 0 and standard deviation 1. 43 Applied Statistics Descriptive Statistics Figure 9 (Source: Internet, Normal curve images) Figure 9, above, shows the grades of students on the z-Scale. Figure 10 displays the Empirical rule using Z-scores.