Step by step solution to "The standard deviation of the data set 4,..."

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2022-01-10

The standard deviation of the data set 4, 6, 2, and 5 is

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Skilled2022-02-09Added 403 answers

The standard deviation of a data set is given as:

$σ = \sqrt{\frac{1}{N} \times \sum_{i = 1}^{N} (x_{i} - \overset{―}{x})^{2}}$

where:

$N$ - number of data;

$\overset{―}{x}$ - mean value

$x_{i}$ - data in data set

To calculate the deviation we can use the following algorythm:

1. Calculate mean $\overset{―}{x}$

2. Calculate $(x_{i} - \overset{―}{x})^{2}$ for all $i$

3. Add all values calculated in $2$

4. Divide the sum by N

5. Get square root to calculate the deviation.

Here we have:

1. $\overset{―}{x}$ $= \frac{4 + 6 + 2 + 5}{4} = \frac{17}{4} = 4.25$

2. $(2 - 4.25)^{2} = (- 2.25)^{2} \approx 5$

$(4 - 4.25)^{2} = (- 0.25)^{2} \approx 0.0625$

$(5 - 4.25)^{2} = (1.25)^{2} \approx 1.6$

$(6 - 4.25)^{2} = (2.25)^{2} \approx 5$

3. Sum is $5 + 0.0625 + 1.6 + 5 \approx 12$

4. $12 \div 4.25 \approx 2.8$

5. $σ = \sqrt{2.8} \approx 1.67$

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