Mathematics 2019 JAMB Past Questions - Question 14: Calculate the standard deviation of the following data 7 8 9 10 11 12 13

Correct Answer

A

Explanation

To calculate the standard deviation of a set of data, you can follow these steps:1. Find the mean of the data set.2. Subtract the mean from each data point to find the deviation of each point from the mean.3. Square each deviation.4. Find the mean of the squared deviations.5. Take the square root of the mean of the squared deviations to find the standard deviation.Let's calculate the standard deviation for the given data set: 7, 8, 9, 10, 11, 12, 13.Step 1: Find the meanMean = (7 + 8 + 9 + 10 + 11 + 12 + 13) / 7Mean = 80 / 7Mean = 11.4286 (rounded to 4 decimal places)Step 2: Find the deviation of each point from the meanDeviation from the mean:-4.4286, -3.4286, -2.4286, -1.4286, 0.5714, 1.5714, 2.5714Step 3: Square each deviation19.6355, 11.7585, 5.9035, 2.0405, 0.3261, 2.4683, 6.6283Step 4: Find the mean of the squared deviationsMean of squared deviations = (19.6355 + 11.7585 + 5.9035 + 2.0405 + 0.3261 + 2.4683 + 6.6283) / 7Mean of squared deviations = 48.7607 / 7Mean of squared deviations = 6.9665 (rounded to 4 decimal places)Step 5: Take the square root of the mean of the squared deviationsStandard deviation = √6.9665Standard deviation ≈ 2.6397 (rounded to 4 decimal places)Therefore, the standard deviation of the given data set is approximately 2.6397.