Which of the following is true about Standard Deviation?
a. It is the maximum value minus the minimum value
b. It a range of values
c. It the average
d. It a measure of spread
e. It measures location
The correct option about Standard Deviation is d. It is a measure of spread.
To understand why, let's first define what standard deviation is. Standard deviation is a statistical measure that quantifies the amount of dispersion or spread in a dataset. It provides valuable information about the variability or diversity of the data values around the mean.
To compute the standard deviation, you would typically follow these steps:
1. Calculate the mean (average) of the dataset by summing up all the values and dividing by the total number of values.
2. For each value in the dataset, calculate the difference between that value and the mean. This difference is called the deviation.
3. Square each deviation obtained in step 2. This step is necessary to ensure that all deviations are positive, as squaring eliminates any negative values.
4. Calculate the mean of the squared deviations obtained in step 3. This value is called the variance.
5. Finally, take the square root of the variance calculated in step 4 to obtain the standard deviation.
Now, let's go back to the options provided:
a. It is the maximum value minus the minimum value: This statement is incorrect. The range is the difference between the maximum value and the minimum value, not the standard deviation.
b. It is a range of values: This statement is incorrect. As mentioned before, the range is the difference between the maximum and minimum values, while the standard deviation measures the spread or dispersion of values around the mean.
c. It is the average: This statement is incorrect. The average or mean is a separate measure that represents the central tendency of a dataset. The standard deviation, on the other hand, quantifies the spread or dispersion of the values around the mean.
d. It is a measure of spread: This statement is correct. The standard deviation is widely used as a measure of spread or variability in a dataset. It provides information on how close or far the values are from the mean.
e. It measures location: This statement is incorrect. The standard deviation does not measure location or central tendency. Instead, it measures the dispersion or spread of the values around the mean.
In conclusion, the correct option is d. It is a measure of spread.