Math Problem Statement

The accompanying data represent the weights​ (in grams) of a random sample of 48​ M&M plain candies. Complete parts​ (a) through​ (f). LOADING... Click the icon to view the weights of the​ M&M plain candies. Question content area bottom Part 1 ​(a) Determine the sample standard deviation weight.

Solution

To determine the sample standard deviation of the weights of the M&M plain candies, the following formula is used:

s=(xix)2n1s = \sqrt{\frac{\sum (x_i - \overline{x})^2}{n-1}}

Where:

  • ss is the sample standard deviation,
  • xix_i are the individual data points (weights),
  • x\overline{x} is the sample mean,
  • nn is the number of data points (48 in this case).

If you provide the list of the M&M weights, I can help you compute the sample standard deviation.

Do you have any questions or want more details on this process?

Here are 5 related questions to explore further:

  1. How is the sample standard deviation different from the population standard deviation?
  2. What is the purpose of using n1n-1 instead of nn in the sample standard deviation formula?
  3. How do outliers affect the standard deviation?
  4. Can the standard deviation be negative?
  5. How do you interpret the value of a standard deviation in the context of this data?

Tip: In real-world data analysis, sample standard deviation is often used when you only have a subset of data from a larger population, while population standard deviation is used when you have the entire data set.

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Math Problem Analysis

Mathematical Concepts

Statistics
Standard Deviation
Data Analysis

Formulas

Sample standard deviation formula: s = sqrt((Σ(x_i - x̄)^2) / (n - 1))

Theorems

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Suitable Grade Level

Grades 11-12, College