To learn more about the size of withdrawals at a banking machine, the proprietor took a sample of 75 withdrawals and recorded the amounts. Determine the mean and standard deviation of these data, and describe what these two Statistics tell you about the withdrawal amounts.
calculations
Mean is measure of central tendency and standard deviation is measure of variability.
To calculate the mean and standard deviation of a set of data, follow these steps:
1. Add up all the values in the data set to find the sum.
2. Divide the sum by the number of data points to find the mean.
3. Subtract the mean from each data point and square the result.
4. Find the sum of all the squared differences.
5. Divide the sum of squared differences by the number of data points.
6. Take the square root of the result to find the standard deviation.
In this case, you have a sample of 75 withdrawals and their corresponding amounts. Let's assume the sample data is as follows:
$20, $50, $100, $80, $70, $30, $60, $90, ...
Step 1: Add up all the values: $20 + $50 + $100 + $80 + $70 + $30 + $60 + $90 + ...
Once you have the sum, move on to step 2.
Step 2: Divide the sum by the number of data points (75 in this case).
Once you have the mean, move on to step 3.
Step 3: Subtract the mean from each data point and square the result: ($20 - mean)^2, ($50 - mean)^2, ($100 - mean)^2, ($80 - mean)^2, ($70 - mean)^2, ($30 - mean)^2, ($60 - mean)^2, ($90 - mean)^2, ...
Step 4: Find the sum of all the squared differences.
Step 5: Divide the sum of squared differences by the number of data points (75 in this case).
Step 6: Take the square root of the result to find the standard deviation.
The mean tells you the average withdrawal amount in the sample, while the standard deviation tells you how much the withdrawal amounts vary from the mean. A higher standard deviation indicates a wider range of withdrawal amounts, while a lower standard deviation indicates a narrower range.