use the five numbers 14, 11, 19, 17, and 14 to complete parts a) through e) below.

a) compute the mean and standard deviation of the given set of data.
the mean is $\bar{x} = $ and the standard deviation is $s = $.
(round to two decimal places as needed.)

Question

use the five numbers 14, 11, 19, 17, and 14 to complete parts a) through e) below.

a) compute the mean and standard deviation of the given set of data.
the mean is $\bar{x} = $ and the standard deviation is $s = $.
(round to two decimal places 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": [ "Mean Calculation", "Sample Standard Deviation" ], "new_concepts": [], "current_concepts": [ "Mean Calculation", "Sample Standard Deviation" ] } ## Calculate the sample mean Using the *Mean Calculation* knowledge point $$ \begin{aligned} \bar{x} &= \frac{\sum x_i}{n} \ \bar{x} &= \frac{14 + 11 + 19 + 17 + 14}{5} \ \bar{x} &= \frac{75}{5} = 15 \end{aligned} $$ ## Calculate the sample standard deviation Using the *Sample Standard Deviation* knowledge point $$ \begin{aligned} s &= \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}} \ \sum (x_i - \bar{x})^2 &= (14-15)^2 + (11-15)^2 + (19-15)^2 + (17-15)^2 + (14-15)^2 \ &= (-1)^2 + (-4)^2 + 4^2 + 2^2 + (-1)^2 \ &= 1 + 16 + 16 + 4 + 1 \ &= 38 \ s &= \sqrt{\frac{38}{5 - 1}} = \sqrt{\frac{38}{4}} = \sqrt{9.5} \approx 3.0822 \end{aligned} $$ Rounding to two decimal places, $s \approx 3.08$. The mean is $\bar{x} =$ $15$ and the standard deviation is $s =$ $3.08$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Sample Standard Deviation" ] }

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Calculate the sample mean

Calculate the sample standard deviation

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