Questions: Find the standard deviation, s, of sample data summarized in the frequency distribution table below by using the formula below, where x represents the class midpoints, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviation to the standard deviation obtained from the original list of data values, 11.1. Standard deviation = (Round to one decimal place as needed.)

Find the standard deviation, s, of sample data summarized in the frequency distribution table below by using the formula below, where x represents the class midpoints, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviation to the standard deviation obtained from the original list of data values, 11.1. Standard deviation = (Round to one decimal place as needed.)
Transcript text: Find the standard deviation, $s$, of sample data summarized in the frequency distribution table below by using the formula below, where $x$ represents the class midpoints, $f$ represents the class frequency, and $n$ represents the total number of sample values. Also, compare the computed standard deviation to the standard deviation obtained from the original list of data values, 11.1. Standard deviation $=$ $\square$ (Round to one decimal place as needed.)
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Solution

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Solution Steps

Step 1: Calculate Class Midpoints

The class midpoints are calculated by averaging the upper and lower bounds of each class interval. Midpoint 1: 1.5

Step 2: Determine Class Frequencies

The class frequencies are given in the frequency distribution table. Frequency 1: 2

Step 3: Compute Total Number of Sample Values

The total number of sample values, $n$, is the sum of all class frequencies: $n = 2$.

Step 4: Calculate Standard Deviation

Using the formula $s=\sqrt{\frac{n[\Sigma(f \cdot x^{2})]-[\Sigma(f \cdot x)]^{2}}{n(n-1)}}$, we find the standard deviation to be $s = 0$.

Step 5: Compare Computed Standard Deviation to Original

The computed standard deviation is lower than the original standard deviation value of 11.1.

Final Answer:

The standard deviation of the sample data from the frequency distribution table is 0, which is lower than the original standard deviation value of 11.1.

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