Calculate the standard deviation of the following marks; 2, 3, 6, 2, 5, 0, 4, 2

Answer Details

To calculate the standard deviation of a set of data, we need to follow these steps: 1. Find the mean (average) of the data. 2. For each data point, subtract the mean and square the result. 3. Find the average of the squared differences (this is called the variance). 4. Take the square root of the variance to find the standard deviation. So, for the given data set {2, 3, 6, 2, 5, 0, 4, 2}, we can first find the mean: (mean) = (2+3+6+2+5+0+4+2)/8 = 24/8 = 3 Next, we can find the squared differences from the mean for each data point: (2-3)^2 = 1 (3-3)^2 = 0 (6-3)^2 = 9 (2-3)^2 = 1 (5-3)^2 = 4 (0-3)^2 = 9 (4-3)^2 = 1 (2-3)^2 = 1 Then we can find the average of these squared differences: (variance) = (1+0+9+1+4+9+1+1)/8 = 26/8 = 3.25 Finally, we take the square root of the variance to find the standard deviation: (standard deviation) = sqrt(3.25) ≈ 1.8 Therefore, the standard deviation of the given marks is approximately 1.8. So the correct option is (c) 1.8.