Math Problem Statement

​Recently, a random sample of 25dash34 year olds was​ asked, "How much do you currently have in​ savings, not including retirement​ savings?" The data in the table represent the responses to the survey. Approximate the mean and standard deviation amount of savings. LOADING... Click the icon to view the frequency distribution for the amount of savings. Question content area bottom Part 1 The sample mean amount of savings is ​$    enter your response here.

Solution

To calculate the sample mean and standard deviation of the savings amounts based on the frequency distribution, follow these steps:

Step 1: Calculate the Sample Mean

The sample mean xˉ\bar{x} is calculated using the formula:

xˉ=(fixi)n\bar{x} = \frac{\sum (f_i \cdot x_i)}{n}

Where:

  • fif_i is the frequency of the ii-th class.
  • xix_i is the midpoint of the ii-th class.
  • nn is the total number of observations.

Step 2: Calculate the Standard Deviation

The standard deviation ss is calculated using the formula:

s=fi(xixˉ)2n1s = \sqrt{\frac{\sum f_i \cdot (x_i - \bar{x})^2}{n - 1}}

To proceed, I need the frequency distribution table that contains the class intervals and their corresponding frequencies. Could you please provide this data?

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Mean
Standard Deviation
Frequency Distribution

Formulas

Sample mean (x̄) = (Σ f_i * x_i) / n
Standard deviation (s) = √[(Σ f_i * (x_i - x̄)^2) / (n - 1)]

Theorems

Central Limit Theorem (underlying the use of the sample mean)
Empirical Rule for standard deviation

Suitable Grade Level

Grades 10-12