4. calculate the standard deviation. round to the nearest tenth on the mean and final answer only.

data set: 59 77 69 61 73 82 67 66 55 89 67 86

Question

4. calculate the standard deviation. round to the nearest tenth on the mean and final answer only.

data set: 59 77 69 61 73 82 67 66 55 89 67 86

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Standard Deviation", "Sample Variance" ], "current_concepts": [ "Standard Deviation", "Sample Variance", "Mean Median Mode" ] } ## Calculate the sample mean $$ \begin{aligned} n &= 12 \ \sum x &= 59 + 77 + 69 + 61 + 73 + 82 + 67 + 66 + 55 + 89 + 67 + 86 = 851 \ \bar{x} &= \frac{851}{12} \approx 70.9167 ightarrow 70.9 \end{aligned} $$ ## Calculate the sum of squared deviations $$ \begin{aligned} \sum (x - \bar{x})^2 &= (59-70.9)^2 + (77-70.9)^2 + (69-70.9)^2 + (61-70.9)^2 \ &+ (73-70.9)^2 + (82-70.9)^2 + (67-70.9)^2 + (66-70.9)^2 \ &+ (55-70.9)^2 + (89-70.9)^2 + (67-70.9)^2 + (86-70.9)^2 \ &= (-11.9)^2 + 6.1^2 + (-1.9)^2 + (-9.9)^2 + 2.1^2 + 11.1^2 \ &+ (-3.9)^2 + (-4.9)^2 + (-15.9)^2 + 18.1^2 + (-3.9)^2 + 15.1^2 \ &= 141.61 + 37.21 + 3.61 + 98.01 + 4.41 + 123.21 \ &+ 15.21 + 24.01 + 252.81 + 327.61 + 15.21 + 228.01 \ &= 1270.92 \end{aligned} $$ ## Calculate the sample standard deviation $$ \begin{aligned} s &= \sqrt{\frac{\sum (x - \bar{x})^2}{n - 1}} \ s &= \sqrt{\frac{1270.92}{11}} = \sqrt{115.5382} \approx 10.7489 ightarrow 10.7 \end{aligned} $$ $10.7$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Statistics", "Standard Deviation" ] }

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Question

Explanation:

Calculate the sample mean

Calculate the sum of squared deviations

Calculate the sample standard deviation

Answer: