2) Consider \( 77,73,75,70,72,76,75,72,74,76 \), Give standord daviation for the number given abave

To calculate the standard deviation of the given data set \( 77, 73, 75, 70, 72, 76, 75, 72, 74, 76 \), we can follow these steps: 1. **Calculate the mean (\(\mu\))**: \[ \mu = \frac{\sum x_i}{N} \] where \(N\) is the number of data points and \(x_i\) are the data points. \[ \mu = \frac{77 + 73 + 75 + 70 + 72 + 76 + 75 + 72 + 74 + 76}{10} = \frac{740}{10} = 74 \] 2. **Calculate the variance (\(\sigma^2\))**: \[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{N} \] First, we calculate each \( (x_i - \mu)^2 \): - \( (77 - 74)^2 = 3^2 = 9 \) - \( (73 - 74)^2 = (-1)^2 = 1 \) - \( (75 - 74)^2 = 1^2 = 1 \) - \( (70 - 74)^2 = (-4)^2 = 16 \) - \( (72 - 74)^2 = (-2)^2 = 4 \) - \( (76 - 74)^2 = 2^2 = 4 \) - \( (75 - 74)^2 = 1^2 = 1 \) - \( (72 - 74)^2 = (-2)^2 = 4 \) - \( (74 - 74)^2 = 0^2 = 0 \) - \( (76 - 74)^2 = 2^2 = 4 \) Now, sum these squared differences: \[ \sum (x_i - \mu)^2 = 9 + 1 + 1 + 16 + 4 + 4 + 1 + 4 + 0 + 4 = 44 \] Now, calculate the variance: \[ \sigma^2 = \frac{44}{10} = 4.4 \] 3. **Calculate the standard deviation (\(\sigma\))**: \[ \sigma = \sqrt{\sigma^2} = \sqrt{4.4} \approx 2.1 \] Thus, the standard deviation of the given data set is approximately \(2.1\).