2.738612788 First, find the mean (average) of all the numbers: 1+2+3+4+5+6+7+8+9 = 45 45 / 9 = 5 Mean is 5 Now take every number and calculate how far it is away from the mean, then square that number 1-5 = -4 ^2 = 16 2-5 = -3 ^2 = 9 3-5 = -2 ^2 = 4 4-5 = -1 ^2 = 1 5-5 = 0 ^2 = 0 6-5 = 1 ^2 = 1 7-5 = 2 ^2 = 4 8-5 = 3 ^2 = 9 9-5 = 4 ^2 = 16 Next, add all the results: 16+9+4+1+0+1+4+9+16 = 60 Then divide by the sample size minus 1 (n-1): 60 / 8 = 7.5 Finally, find the square root of that number: 7.5^ 0.5 = 2.738612788 Answer: 2.738612788
2/9 + 1/3 = 2/9 + 3/9 - Note the equivalence of the fraction 1/3 & 3/9 Add the numerators 5/9 The Answer . 5/9 = 0.555.... ( recurring to infinity as a decimal).
1+4+1+5+9+2+6+5+3+5+8+9+7+9+3+2+3+8+4+6+2+6+4+3+3+8+3+2+7+9+5+0+2+8+8+4+1+9+7+1+6+9+3+9+9+3+7+5+1+0+5+8+2+0+9+7+4+9+4+4+5+9+2+3+0+7+8+1+6+4+0+6+2+8+6
2*9 - 5 = 18 - 5 = 13
With a slope of 2/3, the slope-intercept form of the equation is: y = (2/3)x + b where b is the y-intercept. If it passes through the point (-5, 9) -- I assume that's what you meant in the question -- then you substitute x=-5 and y=9: 9 = (2/3)(-5) + b and solve for b: 9 = -10/3 + b b = 9 + 10/3 = 27/3 + 10/3 = 37/3 So now you have y = (2/3)x + 37/3 Multiply both sides by 3: 3y = 2x + 37 Rearrange: 2x - 3y + 37 = 0 which is standard form ax + by + c = 0
7
You need more than one number to calculate a standard deviation, so 9 does not have a standard deviation.
Variance = 17.9047619 Standard Deviation = 4.23140188
mean =(5+9+10+2+7+9+14)/7=8 s^2 = Variance = (1/7){(5-8)^2+(9-8)^2+(10-8)^2+(2-6)^2+(7-8)^2+(9-8)^2+(14-8)^2}=14.6666 Standard deviation =s= sqrt(14.6666)=3.8297
5.142857143 is the mean.12.43956044 is the variance.3.526976104 is the standard deviation.
The range is 9 and 3.01 is the standard deviation.
7.087547766 is the standard deviation for those figures.
It is approx 2.828
9 15 15 15 16 (five data) Range = 16 - 9 = 7 Mean = (9 + 15 + 15 + 15 + 16)/5 = 70/5 = 14 So we have: (9 - 14)2 = (-5)2 = 25 (the square of the difference of data value and the mean value) (15 - 14)2 = 12 = 1, 3(1) = 3 (16 - 14)2 = 22 = 4, the sum is 32 The standard deviation = √(32/5) ≈ 2.5
(15/sqroot(9))=5 So it is 5
Absolute deviation from what?
Standard deviation is the square root of the sum of the squares of the deviations of each item from the mean, i.e. the square root of the variance. In order to increase the standard deviation, therefore, you need to increase the average deviation from the mean. There are many ways to do this. One is to move each item further away from the mean. For example, take the set [2, 4, 4, 4, 5, 5, 7, 9]. It has a mean of 5 and a standard deviation of 2.14. Multiply each item by 2.2 and subtract 5, giving the set [-1.3, 2.9, 2.9, 2.9, 5, 5, 9.2, 13.4], effectively moving each item 10% further away from the mean. This still has a mean of 5, but the standard deviation is 4.49.