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Range and Standard Deviation Calculator

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Example
Created on 2024-06-20Asked by Elijah Allen (Solvelet student)
Find the range and standard deviation of the data set: 2,4,6,8,10 2, 4, 6, 8, 10 .

Solution

To find the range and standard deviation of the data set 2,4,6,8,10 2, 4, 6, 8, 10 : 1. **Range:** - Identify the maximum and minimum values: Max=10,Min=2. \text{Max} = 10, \quad \text{Min} = 2. - Calculate the range: Range=Max−Min=10−2=8. \text{Range} = \text{Max} - \text{Min} = 10 - 2 = 8. 2. **Standard Deviation:** - Calculate the mean μ \mu : μ=2+4+6+8+105=305=6. \mu = \frac{2 + 4 + 6 + 8 + 10}{5} = \frac{30}{5} = 6. - Find the squared differences from the mean: (2−6)2=16,(4−6)2=4,(6−6)2=0,(8−6)2=4,(10−6)2=16. (2 - 6)^2 = 16, \quad (4 - 6)^2 = 4, \quad (6 - 6)^2 = 0, \quad (8 - 6)^2 = 4, \quad (10 - 6)^2 = 16. - Calculate the variance σ2 \sigma^2 : σ2=16+4+0+4+165=405=8. \sigma^2 = \frac{16 + 4 + 0 + 4 + 16}{5} = \frac{40}{5} = 8. - Calculate the standard deviation σ \sigma : σ=8=22. \sigma = \sqrt{8} = 2\sqrt{2}. Therefore, the range is 8 and the standard deviation is 22 2\sqrt{2} . Solved on Solvelet with Basic AI Model
Some of the related questions asked by Scarlett Hill on Solvelet
1. Calculate the range of a dataset: {2,5,7,9,12} \{2, 5, 7, 9, 12\} .2. Find the standard deviation of a dataset: {15,18,21,24,27}\{15, 18, 21, 24, 27\}.
DefinitionA data set with the lowest value of 70 and the highest value of 98 has a range of 98 - 70 = 28. Standard dev. is the way to measure the dispersion or the spread of a set of values around the mean. Eg : For a data set of the type {2,4,6,8,10}, the range= 10−2 = 8 and the standard deviation will be approximately 2.83
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