Chapter 12 Summarizing Test Scores: Measures of Central Tendency

The Mean

            Measures of central tendency provide a single summary figure that best describes the central location of an entire distribution of test scores. The mean, however, is the most popular among the measures of central tendency. This oftentimes called arithmetic average.

            Mean for Ungrouped Test Scores. When test scores are ungrouped that is N is 30 or less, mean is computed following the formula

                                                M=Sx/N

Where: M= mean

            Sx= Sum of test scores

            N= total number of test scores or cases

Let us illustrate the computation of the mean for ungrouped test scores. For instance the following scores were obtained by Grade VI pupils in a spelling test: 12, 11, 10,9, 7, 15, 8, 6, 14, 13. What is the mean score of the pupils in the aforementioned spelling test? To compute the mean, we first have to add the scores (Sx=105) and count the number of scores (N=10). Let us plug in the obtained values into our computational formula.

                                                                        M=Sx/N

                                                                            = 105/10

                                                                            =10.5

Mean for Grouped Test Scores. When test scores are more than 30, the abovementioned computational formula is no longer applicable. There are two ways of computing the mean grouped test scores: frequency-class mark method; and the deviation method.

            To compute the mean using the frequency-class marked method, the following steps have to observed:

1.      Calculate the class mark or midpoint of each class interval.

2.      Multiply each class mark by its corresponding frequency

3.      Sum up the cross products of the class mark and frequency of each class.

4.      Count the number of cases or total number of scores.

5.      Plug into the computation formula the values obtained in steps 3 and 4. The formula to be applied is given below:

M= Sfcm/N

Where: M= the mean

            f= frequency of a class

            cm= class mark or midpoint of a class

            N= total number of scores or cases

            Sfcm= sum of the cross products of the frequency and class mark.

Table 12.1 shows how the mean for grouped data is computed using the frequency-class mark method.

Table 12.1

Computation of the Mean Via the Frequency-Midpoint Method

Classes	Frequency(f)	Class Mark(cm)	fcm
46-50 41-45 36-40 31-35 26-30 21-25 16-20 11-15	5 7 9 10 8 6 4 4	48 43 38 33 28 23 18 13	240 301 342 330 224 138 72 52
	N=53		Sfcm=1699

Going over Table 12.1 it can be seen that the frequency of each class is shown in the second column. Class mark is shown in column 3 and is obtained by adding the lower and upper limits of each class and dividing the sum by 2. On the last column are the cross products of each frequency and class mark. The sum of the cross products is 1,699. Let us substitute the values into our computational formula to obtain the mean.

M=Sfcm/N