which has a larger standard deviation: the distribution of weekly allowances to 12-year olds or the distribution of monthly household mortgage payments?
To determine which distribution has a larger standard deviation, you will need to compare the variability or spread of the two distributions. The standard deviation measures the extent to which the values in a distribution deviate from the mean.
To find the standard deviation of the two distributions, you will need the following information:
1. For the distribution of weekly allowances to 12-year olds:
- Obtain data on the weekly allowances given to 12-year olds. This could be a sample or population data.
- Calculate the sample standard deviation using the formula:
Standard Deviation = √(Σ(xi - x̄)² / (n - 1))
Here, xi represents each value in the data set, x̄ is the mean of the data set, Σ denotes the sum of the values, and n is the number of data points.
2. For the distribution of monthly household mortgage payments:
- Collect data on the monthly mortgage payments made by households. Again, this could be a sample or population data.
- Compute the sample standard deviation using the same formula as above.
After calculating the standard deviations for both distributions, compare the values. The distribution with the larger standard deviation will have a greater spread and thus more variability.
Keep in mind that this explanation assumes you have access to the data for both distributions. If you don't, you may need to find sources or collect the required data first.