Explained: "Find the range and standard deviation of the..."

High School
Statistics and Probability
High school statistics
Data distributions

Antinazius

Answered question

2021-11-29

Find the range and standard deviation of the set of data.
11,9,7,11,12

Answer & Explanation

George Spencer

Beginner2021-11-30Added 12 answers

Step 1
Given data,
11,9,7,11,12
Range =?
Sd=?
Step 2
Range $= M a x - M i n$
Range $= 12 - 7$
Range $= 5$
Standard deviation is ?
Mean is
$μ = \frac{\sum x}{n}$
$= \frac{50}{5}$
$= 10$
Standard deviation is
$σ = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {(x_{i} - μ)}^{2}}$
$σ^{2} = \frac{\sum {(x_{i} - μ)}^{2}}{N}$
$= \frac{{(11 - 10)}^{2} + \dots + {(12 - 10)}^{2}}{5}$
$= \frac{16}{5}$
$= 3.2$
$σ = \sqrt{3.2}$
$= 1.7888543819998$

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