Question

Describe in a meaningtul manner what the correlations, means and standard deviations, in the table below, convey about this class of 3015 students. (7) Variables Test 1 ASS1 Test 2 Mean SD Test 1 49. 69 68.53 17.19 ASS1 38° 63.02 16.98 Test 2 61.11 20.22 Note. ASS1 - Assignment 1. Test 1, ASS 1, and Test 2 grades as a percent. *p<.05.

Answer 1

Correlation gives the degree and direction of relationship between two variables. It lies between -1 and 1.

If correlation is positive, it means as one variable increases, the other also tends to increase and if it is negative, increase in one variable tends to decrease in the other. As the absolute value of correlation nears 1, it means the degree of relationship is higher.

Mean is a measure of central tendency. It is the mathematical average of a given set of values. It is calculated as the sum of observations divided by total number of observations.

Standard deviation is a measure of dispersion. It shows how much a data is scattered about its means. High standard deviation means the data is highly dispersed about its mean and vice versa.

In the given table, ASS1 gives scores of the students in Assignment 1, Test 1 and Test 2 are scores of the students in two tests.

The correlation between Test 1 and ASS1 is 0.49. So, the scores in Test 1 and ASS1 are positively correlated. It means if a student has high score in test1, his score in assignment 1 also tends to be higher.

The correlation between Test 1 and Test 2 is 0.69. So, the scores in Test 1 and Test 2 are positively correlated. It means if a student has high score in test1, his score in test 2 also tends to be higher. Also the degree of relationship is higher than that of between ASS1 and Test 1.

The correlation between ASS1 and Test 2 is 0.38. So, the scores in ASS1 and Test 2 are positively correlated. It means if a student has high score in assignment 1, his score in test 2 also tends to be higher. Also the degree of relationship is lower than that of between ASS1 and Test 1 and lower that of between Test 1 and Test 2

The mean score of the 3015 students in Test 1 is 68.53, that in ASS1 is 63.02 and that in Test 2 is 61.11.

It means that on average, the students performed better in Test 1 than in both others. Also the worst performance on average was in Test 2. The average performance in assignment 1 was better than Test 2 but poor when compared to Test 1.

The standard deviations of Test 1 , ASS1 and Test 2 are 17.19,16.98 and 20.22 respectively.

So, the marks in Test 2 is more dispersed about the mean , followed by marks in Test 1 and marks in ASS1 is the least dispersed among the three.