Given the following students\' test scores (95, 92, 90, 90, 83, 83, 83, 74, 60,

Question

Given the following students' test scores (95, 92, 90, 90, 83, 83, 83, 74, 60, and 50), identify the mean, median, mode, range, variance, and standard deviation for the sample. Write a 500-750-word summary and analysis discussing the results of your calculations. State your results for the sample: the mean, median, mode, range, variance, and standard deviation Explain which method is best for this data set. Why? Conduct a one sample T-test and interpret the results. In what situations would this information be useful?

Explanation / Answer

Compute mean:(95+92+....+50)/10=80

Median: Arrange the data in ascending order. 50, 60, 74, 83, 83, 83, 90, 90, 92, 95. The data set is even in number, so median is average of two middle most numbers; (83+83)/2=83.

Mode refers to frequently occuring data in the set. That is 83.

Range: Maximum-minimum=95-50=45

Variance: Summation1/n[(Xi-Xbar)^2]=summation 1/10[(50-80)^2+...+(95-80)^2]=214.667

Standard deviation=sqrt Var=14.651

The students' test score ranges from minimum 50 to maximum 95 in a sample of 10 students. The mean is 80 and the median is 83, this reflects scores are left skewed. Since, distribution is skewed, median seems to be fit as a measure of central tendency and so is the range. The value of mode indicates that the score value 83 is most common among students scores. The standard deviation indicates that the difference of each scores of students from its' average is around 14.651. The measure of dispersion is high because of the lower most score, 50.

Median and range is best descriptive measure for th edata set.

From information given, Xbar=80, mu=83, sigma=14.651, n=10

t=(Xbar-mu)/(s/sqrt n-1)=(80-83)/(14.651/sqrt10)=-0.647

The p value is 0.266, not less than alpha=0.05. Therefore, fail to reject null hypothesis (H0: mu=83 versus H1:mu ot equal to 83), to conclude that there is not sufficient sample evidence to conclude that mean score is not equal to 83.

If students are randomly sampled and the distribution of their scores is nearly normal.

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