Savings Recently, a random sample of 25–34 year olds was asked, “How much do you currently have in savings, not including retirement savings?” The following data represent the responses to the survey. Approximate the mean and standard deviation amount of savings.

Verified step by step guidance

1. Step 1: Organize the data collected from the sample of 25–34 year olds. List all the individual savings amounts reported in the survey to have a clear dataset to work with.
2. Step 2: Calculate the mean (average) savings amount using the formula: \[\text{Mean} = \frac{\sum_{i=1}^n x_i}{n}\] where \(x_i\) represents each individual savings amount and \(n\) is the total number of respondents.
3. Step 3: Find the deviations of each savings amount from the mean by subtracting the mean from each individual value: \[d_i = x_i - \text{Mean}\]
4. Step 4: Calculate the squared deviations for each data point: \[d_i^2 = (x_i - \text{Mean})^2\]
5. Step 5: Compute the sample standard deviation using the formula: \[s = \sqrt{\frac{\sum_{i=1}^n d_i^2}{n - 1}}\] This measures the spread of the savings amounts around the mean.

Key Concepts

Sample Mean

The sample mean is the average value of a data set, calculated by summing all observations and dividing by the number of observations. It provides a measure of central tendency, representing the typical amount of savings in this context.

Sample Standard Deviation

The sample standard deviation measures the spread or variability of data points around the sample mean. It is calculated by taking the square root of the average squared deviations from the mean, indicating how much individual savings amounts differ from the average.

Random Sampling

Random sampling ensures that every individual in the target population has an equal chance of being selected. This reduces bias and allows the sample statistics, like mean and standard deviation, to be valid estimates of the population parameters.