What is the significance of understanding of distribution’s range, skewness, and

Question

What is the significance of understanding of distribution’s range, skewness, and kurtosis?

Concerning a distribution of scores, what is the significance of determining basic measures of central tendency involving the mean, median, and mode?

Concerning a distribution of scores, what is the significance of determining basic measures of variability involving the range, standard deviation, and standard error of measurement?

Concerning distribution of scores, what is the significance of determining basic measures of variability involving a percentile, a stanine, and a standardized score (i.e., t-score, z- score)?

Describe the difference between criterion- referenced assessment and a standardized norm-referenced assessment.

Describe the difference between a criterion-referenced grade- equivalent score and a standardized norm-referenced score.

Explanation / Answer

Range; Range is defined as the highest value of the given distribution minus the lowest value of the given distribution. It is simple representative of understanding the dispersion of the distribution. Since this was based on only two observations it gives only the length of the spread of the distribution, that is minimum and maximum values of the distribution. But not gives a a precise measure of the variablilty.

Skewness; This is a measure of the asymmetry of the distribution. It gives idea whether the data points uniformly lie eitherside of the central value, i.e most commonly mean or not.So understanding theskewness of the dataset indicates whether the deviations from mean are positive or negative If there is no positive or negative deviation we can say it is normally distributed otherwise we can say it is positive or negative skewed based on the positive or negative deviation. This gives better picture of the variablilty of the distribution and it has benefit in many areas.

Many models use nomal distribution. Even though the distribution is not symmetrical (skewed) but can use the normal approximation when the distribution of values are large.

Kurtosis:This is a measure of the tallerness of the symmetric distribution. It give better picture of the shape of the normal distribution. whether the distribution is more peak, or normal or flat.

Karl pearson suggested a measure, based on this if the value is 3 we can say it is normal , if greater than 3 it is called as leptokurtic, if it is less than 3 it is called platykurtic.

It gives idea about the extreme observation of the data set. In otherwords, whether the distribution has extreme outlier or not. if the distribution has extreme outlier, we'll decide the correct/alternative statistical treatment to go on.

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