Histogram of Distribution of Total Points

Histograms are a type of graphs that clearly show the frequency distribution of a data set. The histogram may include important information such as the skewness of the graph as well as if it contains outliers; it helps to explain the data and its results through a matter of peaks and frequency. As the book of the SPSS described the histograms as, “they indicate the number of subjects or cases in ranges of values for a continuous variable, such as the number of students who scored between 90 and 100, between 80 and 89 and so forth on a final exam”(). In this case and the histograms that are listed above which shows the performance of gender on the total class grade. Histograms are very beneficial especially when there is a large data set and they must be included in the graph; thus, histograms list the number of subjects within a range of values, for example the histograms above, the total points were broken down to fit all the scores and it shows the value range as students who scored between 40 to 60, between 60 and 80, between 100 and 120 and so forth. For the male hisogram, its negatively skewed because the majority of values lie above the mean. However the female histogram shows a normal distribution that is symmetric about the average value. The highest peak falls between the plus and minus standard deviation of the mean (). The male histogram is not symmetry because the highest peak does not fall between the plus and minus. “ Kurtosis is a measure of peakness or the flatness of a distribution; a kurtosis value near zero indicates a shape close to normal as the positive value for the kurtosis indicates a distribution more peaked than normal” the female histogram shows a positive kurtosis because of  the high peak that is called the “ Leptokurtic Kurtosis” whereas the male histogram shows a negative kurtosis because it indicated a flatter shape than normal (Platkurtic Kurtosis). The male histogram includes an outlier between 40 and 60 total points as it shows that only one person had total points of 50 in the class. Whereas the female histogram shows two outliers between 40 and 60, 60 and 80. Both histograms show outliers that are close to the zero 0. Outliers occur due to an error in the data set; however, outliers could also occur by chance in the distribution that’s why researchers or data collector may ensure the quality and correctness of the data from the original set before its moved to the SPSS to avoid outliers or any other measurement errors.  Both histograms involve modality as they have one high peak in the distribution, which is called the unimodal. The overall results showed that in average females showed better performance in the total points than males as there are more females had better scores than males in the total score of the class.

·         Indicate which variables are meaningless to interpret in terms of mean, standard deviation, skewness, and kurtosis. Justify your decision.

·         Next, indicate which variables are meaningful to interpret. Justify your decision.

·         For the meaningful variables, do the following:

o    Specify any variables that are in the ideal range for both skewness and kurtosis.

o    Specify any variables that are acceptable but not excellent.

o    Specify any variables that are unacceptable. 

o    Explain your decisions.

·         For all meaningful variables, report and interpret the descriptive statistics (mean, standard deviation, skewness, and kurtosis).

the mean is influenced by the distribution skewness; the median is more appropriate for skewed data to show results of the overall data

std is important for symmetric data

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