the numbers of regular season wins for 10 football teams in a given season are given below. determine the range, mean, variance, and standard deviation of the population data set.

2, 10, 15, 2, 12, 10, 12, 8, 4, 8

the range is
(simplify your answer.)

Question

the numbers of regular season wins for 10 football teams in a given season are given below. determine the range, mean, variance, and standard deviation of the population data set.

2, 10, 15, 2, 12, 10, 12, 8, 4, 8

the range is
(simplify your answer.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Range Calculation", "Mean Calculation", "Population Variance", "Population Standard Deviation" ], "new_concepts": [], "current_concepts": [ "Range Calculation", "Mean Calculation", "Population Variance", "Population Standard Deviation" ] } ## Calculate the range Using the *Range Calculation* knowledge point $$ \begin{aligned} &\text{Dataset: } \{2, 10, 15, 2, 12, 10, 12, 8, 4, 8\}\ &\text{Maximum value } = 15\ &\text{Minimum value } = 2\ &\text{Range} = 15 - 2 = 13 \end{aligned} $$ ## Calculate the population mean Using the *Mean Calculation* knowledge point $$ \begin{aligned} &N = 10\ &\sum x = 2 + 10 + 15 + 2 + 12 + 10 + 12 + 8 + 4 + 8 = 83\ &\mu = \frac{83}{10} = 8.3 \end{aligned} $$ ## Calculate the population variance Using the *Population Variance* knowledge point $$ \begin{aligned} &\sum (x - \mu)^2 = (2-8.3)^2 + (10-8.3)^2 + (15-8.3)^2 + (2-8.3)^2 + (12-8.3)^2 \ &\phantom{\sum (x - \mu)^2 =} + (10-8.3)^2 + (12-8.3)^2 + (8-8.3)^2 + (4-8.3)^2 + (8-8.3)^2\ &\sum (x - \mu)^2 = 39.69 + 2.89 + 44.89 + 39.69 + 13.69 + 2.89 + 13.69 + 0.09 + 18.49 + 0.09 = 176.1\ &\sigma^2 = \frac{176.1}{10} = 17.61 \end{aligned} $$ ## Calculate the population standard deviation Using the *Population Standard Deviation* knowledge point $$ \begin{aligned} &\sigma = \sqrt{17.61} \approx 4.20 \end{aligned} $$ The range is 13 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Range Calculation" ] }

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Question

Explanation:

Calculate the range

Calculate the population mean

Calculate the population variance

Calculate the population standard deviation

Answer: