Question

Use a calculator to find the standard deviation of this data eight, 14, 12, nine, 16 round to the nearest 10th

Answer 1

To find the standard deviation of a data set, calculate the mean, subtract the mean from each value and square the result, calculate the sum of the squared differences, divide by the number of values, and take the square root. Round the result to the nearest tenth.

Step-by-step explanation:

To find the standard deviation of the given data: 8, 14, 12, 9, 16, you can use a calculator. Here are the steps:

1. Calculate the mean (average) of the data set. Add up all the values and divide by the number of values.
2. Subtract the mean from each value in the data set and square the result for each value.
3. Calculate the sum of all the squared differences.
4. Divide the sum by the number of values.
5. Take the square root of the result to get the standard deviation.
6. Round the standard deviation to the nearest tenth.

Using a calculator, the mean of the data set is 11.8. Subtracting the mean from each value and squaring the differences gives us: 8, 2.4, 0.8, 5.8, 19.6. The sum of these squared differences is 36.6. Dividing by the number of values (5) gives us 7.32. Taking the square root of 7.32 gives us approximately 2.7. Rounding to the nearest tenth, the standard deviation is 2.7.