Statistics

Step 1: Calculate the mean.
First, calculate the mean of the data set:
Step 2: Calculate the squared differences from the mean.
Next, calculate the squared differences from the mean for each observation:
Step 3: Calculate the variance.
Variance is the average of these squared differences:
Step 4: Calculate the standard deviation.
The standard deviation is the square root of the variance:
Step 5: Conclusion.
Therefore, the standard deviation is . The correct answer is (4) 2.

Step 1: Mode formula in terms of mean and median.
The mode of a distribution can be calculated using the empirical relationship:
Step 2: Applying the values.
Given that the mean = 17 and the median = 18, we substitute these values into the formula:
Step 3: Conclusion.
Therefore, the mode of the distribution is . The correct answer is (3) 18.5.