how do you get a standard deviation of 1.04563 when the sum of x=238, n=25 and the mean is 9.52
Please read and follow directions.
With your data, you don't, unless you meant
∑(mean-x)^2 = 238
You have to subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
To find the standard deviation, you need to follow these steps:
1. Calculate the variance: Begin by subtracting the mean from each value of x and squaring the result. Then, sum all the squared differences.
- In this case, let's call the squared differences "d" and calculate them for each value of x:
d1 = (x1 - mean)^2
d2 = (x2 - mean)^2
d3 = (x3 - mean)^2
.
.
.
d25 = (x25 - mean)^2
Then, sum all these squared differences: sum(d1 + d2 + d3 + ... + d25).
2. Divide the variance by (n-1): In this case, since n = 25, you will divide the sum of squared differences by 24 (25-1).
variance = sum(d1 + d2 + ... + d25) / (n-1)
3. Take the square root of the variance to get the standard deviation:
standard deviation = sqrt(variance)
To get a standard deviation of 1.04563 with the given values, you would need to calculate the sum of squared differences that results in this variance.