Math Problem Statement

Calculate in tabular format

Calculate standard deviation for the data set 4, 11, 18, 25, 32.

Solution

It looks like you've uploaded an image asking for the calculation of the standard deviation for the data set 4,11,18,25,324, 11, 18, 25, 32. Let's solve this in tabular format.

Steps to calculate Standard Deviation:

  1. Find the mean (average) of the numbers.
  2. Calculate each data point's deviation from the mean.
  3. Square each deviation.
  4. Find the average of these squared deviations (this is the variance).
  5. Take the square root of the variance to find the standard deviation.

Data set: 4,11,18,25,324, 11, 18, 25, 32

Let's proceed to calculate the standard deviation using a table.

xix_i (Data)xixˉx_i - \bar{x} (Deviation from Mean)(xixˉ)2(x_i - \bar{x})^2 (Squared Deviation)
4
11
18
25
32

I'll calculate each step and fill the table now.Here is the tabular breakdown for the standard deviation calculation of the data set 4,11,18,25,324, 11, 18, 25, 32:

xix_i (Data)xixˉx_i - \bar{x} (Deviation from Mean)(xixˉ)2(x_i - \bar{x})^2 (Squared Deviation)
4-14196
11-749
1800
25749
3214196
  • Mean: xˉ=18\bar{x} = 18
  • Variance: 9898
  • Standard Deviation: 9.909.90

Would you like further explanation or have any questions about this?

Here are some questions to expand on:

  1. What is the difference between population and sample standard deviation?
  2. How does standard deviation differ from variance?
  3. In what situations is it important to use standard deviation over other measures of spread?
  4. Can the standard deviation ever be negative?
  5. How does standard deviation behave with outliers?

Tip: Always check if you're calculating for a population or a sample, as formulas differ slightly!

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Math Problem Analysis

Mathematical Concepts

Statistics
Standard Deviation
Variance

Formulas

Mean: (sum of data points) / (number of data points)
Variance: (sum of squared deviations from the mean) / (number of data points)
Standard Deviation: square root of variance

Theorems

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Suitable Grade Level

Grades 9-12