Using the frequency distribution provided below, calculate the standard deviation using the formula, where xx denotes the class midpoint, ff is the class frequency, and nn represents the total number of sample values. Use the formula s=n[Σf⋅x2]−[Σ(f⋅x)]2n(n−1)s=\sqrt{\frac{n\left\lbrack\Sigma f\cdot $$x^2$$\right\rbrack-\left\lbrack\Sigma\left(f\cdot x\right)\right\$$rbrack^2$$}{n\left(n-1\right)}}.Then, compare your calculated standard deviation with the value of 14.9014.90 obtained using the sum of squares of deviations formula.

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Levels of Measurement
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2. Describing Data with Tables and Graphs(0)

Visualizing Qualitative vs. Quantitative Data
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Frequency Distributions
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Histograms
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Bar Graphs and Pareto Charts
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Time-Series Graph
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Mean
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Median
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Mode
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Interpreting Standard Deviation
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3. Describing Data Numerically

Standard Deviation

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Problem 23Multiple Choice

Using the frequency distribution provided below, calculate the standard deviation using the formula, where $x$ denotes the class midpoint, $f$ is the class frequency, and $n$ represents the total number of sample values. Use the formula $s = \sqrt{\frac{n [Σ f \cdot x^{2}] - {[Σ (f \cdot x)]}^{2}}{n (n - 1)}}$ .

Then, compare your calculated standard deviation with the value of $14.90$ obtained using the sum of squares of deviations formula.

$s equals 14.90$

The standard deviation from the frequency distribution is identical to the standard deviation from the original data

$s equals 13.95$

The standard deviation from the frequency distribution is slightly lower than the standard deviation from the original data due to class grouping

$s equals 19.50$

The standard deviation from the frequency distribution is significantly higher than the standard deviation from the original data

$s equals 6.75$

The standard deviation from the frequency distribution is significantly lower than the standard deviation from the original data

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