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 13.
(simplify your answer.)

the population mean is 8.3.
(simplify your answer. round to the nearest tenth as needed.)

the population variance is
(simplify your answer. round to the nearest tenth as needed.)

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 13.
(simplify your answer.)

the population mean is 8.3.
(simplify your answer. round to the nearest tenth as needed.)

the population variance is
(simplify your answer. round to the nearest tenth as needed.)

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" ], "new_concepts": [], "current_concepts": [ "Range Calculation", "Mean Calculation", "Population Variance", "Population Standard Deviation" ] } ## Identify the given population data set Using the *Range Calculation* and *Mean Calculation* knowledge points $$ N = 10,\quad X = \{2, 10, 15, 2, 12, 10, 12, 8, 4, 8\} $$ ## Calculate the range of the data set Using the *Range Calculation* knowledge point $$ \begin{aligned} &\text{Maximum value} = 15\ &\text{Minimum value} = 2\ &\text{Range} = 15 - 2 = 13 \end{aligned} $$ ## Calculate the population mean Using the *Mean Calculation* knowledge point $$ \begin{aligned} &\sum X = 2 + 10 + 15 + 2 + 12 + 10 + 12 + 8 + 4 + 8 = 83\ &\mu = \frac{\sum X}{N} = \frac{83}{10} = 8.3 \end{aligned} $$ ## Calculate the population variance Using the *Population Variance* knowledge point $$ \begin{aligned} &\sum (X - \mu)^2 = (2-8.3)^2 + (10-8.3)^2 + (15-8.3)^2 + (2-8.3)^2 + (12-8.3)^2 \ &\phantom{\sum (X - \mu)^2 =} + (10-8.3)^2 + (12-8.3)^2 + (8-8.3)^2 + (4-8.3)^2 + (8-8.3)^2\ &\sum (X - \mu)^2 = (-6.3)^2 + (1.7)^2 + (6.7)^2 + (-6.3)^2 + (3.7)^2 \ &\phantom{\sum (X - \mu)^2 =} + (1.7)^2 + (3.7)^2 + (-0.3)^2 + (-4.3)^2 + (-0.3)^2\ &\sum (X - \mu)^2 = 39.69 + 2.89 + 44.89 + 39.69 + 13.69 + 2.89 + 13.69 + 0.09 + 18.49 + 0.09 = 176.1\ &\sigma^2 = \frac{\sum (X - \mu)^2}{N} = \frac{176.1}{10} = 17.61 \approx 17.6 \end{aligned} $$ The population variance is $17.6$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Population Variance" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given population data set

Calculate the range of the data set

Calculate the population mean

Calculate the population variance

Answer: