Orhan SELEN - 120103017 - ELT 1-A 4th Portfolio Assignment - Mean,mode,median and standart deviation

Teachers use lots of ways to determine whether a test is reliable and valid. Mathematical calculations often help a teacher to measure these two terms.

Arithmetic mean is briefly the most frequent value in a data set. In this explanation,the data is the scores of the students that teachers get through assessing,using a test. The most frequent value is calculated through adding all the scores to eachother and divide this sum to the number of the scores we used. This gives us an average score of this particular data set.

Median is the middle value in a list. The number of the values in this list can either be an odd or even number. For odd amount of values,just sorting the data in the incrementing order and grouping them two from left and two from right everytime will leave us one value left which is the median. For even amount of values, it is enough to add the two middle numbers to eachother and divide them to find the median.

Mode refers to the number which repeats more frequent than the other numbers. This is used to find out how many people got the same score after a test.

Standard deviation in a data set refers to how close or how far the items in the data set are,to the mean(average) of this data set. This is used to find out an "explanation" for the scores and also reflects the reliability of a test.

It is better to explain all these terms with a set of simple calculations. Lets assume that there are ten students in one classroom and they are assessed through a test with 25 multiple choice questions . In the end,they get a score based on their doings. While reading,a teacher may ask himself/herself the probability whether the test was too "easy" or too "hard". Sure,there are lots of stuff to be considered before easiness or hardness of the test but since the test is done,there is no way back.Here are the grades of the students and calculations next to the grades.

According to the graph , the test was fair,not too easy,not that hard. Various ways can be used to find out the reliability of test but statistics often help to check it in an easier way. Teachers,whose tests have equally distributed graphs,should continue to apply these tests. Comparisons with other classes at the same knowledge should not be different too much. If there is less difference,this will mean that the test can become a standardized one.

http://www.robertniles.com/stats/stdev.shtml is used to understand and explain standart deviation.http://www.mathsisfun.com/median.html is used to understand and explain median.