find the range and standard deviation of the set of data.

10, 10, 5, 12, 23

the range is .
(simplify your answer.)

the standard deviation is .
(round to the nearest hundredth as needed.)

Question

find the range and standard deviation of the set of data.

10, 10, 5, 12, 23

the range is  .
(simplify your answer.)

the standard deviation is  .
(round to the nearest hundredth as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Measures of Dispersion", "Sample Standard Deviation" ], "new_concepts": [], "current_concepts": [ "Measures of Dispersion", "Sample Standard Deviation" ] } ## Calculate the range Using the *Measures of Dispersion* knowledge point $$ \begin{aligned} &\text{Data set: } \{10, 10, 5, 12, 23\}\ &\text{Maximum value } = 23\ &\text{Minimum value } = 5\ &\text{Range} = 23 - 5 = 18 \end{aligned} $$ ## Calculate the sample mean Using the *Sample Mean Symbol* knowledge point $$ \begin{aligned} &n = 5\ &\bar{x} = \frac{10 + 10 + 5 + 12 + 23}{5} = \frac{60}{5} = 12 \end{aligned} $$ ## Calculate the squared deviations Using the *Sample Standard Deviation* knowledge point $$ \begin{aligned} &(10 - 12)^2 = (-2)^2 = 4\ &(10 - 12)^2 = (-2)^2 = 4\ &(5 - 12)^2 = (-7)^2 = 49\ &(12 - 12)^2 = 0^2 = 0\ &(23 - 12)^2 = 11^2 = 121 \end{aligned} $$ ## Calculate the sample variance and standard deviation Using the *Sample Standard Deviation* knowledge point $$ \begin{aligned} &\sum (x_i - \bar{x})^2 = 4 + 4 + 49 + 0 + 121 = 178\ &s^2 = \frac{178}{5 - 1} = \frac{178}{4} = 44.5\ &s = \sqrt{44.5} \approx 6.6708 \end{aligned} $$ The range is 18. The standard deviation is 6.67. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Sample Standard Deviation" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the range

Calculate the sample mean

Calculate the squared deviations

Calculate the sample variance and standard deviation

Answer: