Score # of students

------- ---------------

83....................5

70....................6

92....................3

X.....................5

64....................1

83-78=5 5*5=25

70-78=-8 -8*6=-48

92-78=14 14*3=42

78-64=14 -14*1=-14

Sum=25-48+42-14=5 5x=5 x=1 and then the average is 79

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I might have to repeat what was posted earlier which is very useful for my explanation below. So, please refer to the above table.

In the formula, x represents individual numbers Or scores in this problem.

Mean is the average which is given as 78 (in this problem).

The average or mean is given as 78.

The scores(numbers) are 83,83,..(5 times because there are 5 students who got 83), 70,70..(6times), 92., 92, 92, X (5 times), and 64.

Keep in mind that deviations are positive and negative and the sign is important.

The deviation of 83 from the mean is 83-78 = 15

because we have 5 students who scored 83, To add up the deviations of scores of these 5 students, we need to multiply 15 by 5.

So, you have 15 * 5 = 75.

Similarly, the deviation of 70 is 70-78 = -8.

Since, there are 6 students with this score, toal deviation for these 6 scores is -8*6 = -48

Similarly, the deviation of 92 is 92-78 = 14

Total deviation of 3 scores = 14*3=42

Let the deviation of X is y. Total deviation of 5 such scores is 5y.

The deviation of 64 is 64-78=-14.

The sum of all deviations is 15-48+42+5y-14.

This SUM should be Zero.

ie 15-48+42+5y-14=0.

ie 5y=5

is y=1.

Note that y is positive and y is only a deviation not the actual score (the answer).

In fact, the deviation y can be written as X-78.

therefore, X-78=1 or X = 79.

The earlier post did give you a nice table. I have the explanation for it.

Now, you have both. Hopefully it makes sense now.

-Srinivas.

july05 wrote:

Srinivas,

could you please show how to work this formula using this problem?

thanks a lot.