If the standard deviation for this set of data 1,3,4,4,6,7,8,9,9,9 is 2.86744, should it be rounded to 2.9 or 2.87?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The standard deviation of a given group of values is calculated in the following way.

First, determine the average of the values. Here, the values are 1, 3, 4, 4, 6, 7, 8, 9, 9, 9.

The average of the values is (1+3+4+4+6+7+8+9+9+9)/10 = 60/10 = 6.

Next, find the square of the difference of each value and the average.

(1-6)^2 = 25, (3-6)^2 = 9, (4-6)^2 = 4, (4 - 6)^2 = 4, (6 - 6)^2 = 0, (7 - 6)^2 = 1, (8 - 6)^2 = 4, (9 - 6)^2 = 9, (9 - 6)^2 = 9, (9 - 6)^2 = 9

Add the values obtained and find the square root of their sum divided by (number of values - 1)

sqrt[(25 + 9 + 4 + 4 + 0 + 1 + 4 + 9 + 9 + 9)/9] = sqrt(74/9) = 2.86744

If you want to round this, the number of decimal digits that you keep is dependent on how accurate you want the final result to be. You can round it to 2.87, or 2.9 or even 3.

The standard deviation got can be rounded to either 2.9 or 2.87 based on the accuracy required.

taangerine's profile pic

taangerine | Student, Grade 12 | (Level 1) Valedictorian

Posted on

Both would work, but it really depends on what type you are working on and what is requested from the initial work. If it tells you to round, then round. But, if it needs to be specific, going out further in the decimal places would be better. 

eli468's profile pic

eli468 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

Typically if a teacher doesn't tell you a required decimal place they want you to go to, then the more accuracy the better. Either answer would work, but unless specified it might be best to use 2.87. Especially if you are doing lab work, then, typically, going out to the further decimal place is better for doing equations and formulas.

zumba96's profile pic

zumba96 | Student, Grade 11 | (Level 3) Valedictorian

Posted on

Either will work based on what you are trying to round to. If you are rounding just to the tenths then your first option is better. Both are right but you need to find which the decimal needs to be rounded to 

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