use the five numbers 18, 15, 12, 13, and 12 to complete parts a) through e) below.

a) compute the mean and standard deviation of the given set of data.

the mean is $\bar{x} = 15$ and
(round to two decimal places as needed.)

Question

use the five numbers 18, 15, 12, 13, and 12 to complete parts a) through e) below.

a) compute the mean and standard deviation of the given set of data.

the mean is $\bar{x} = 15$ and
(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 $$ \begin{aligned} n &= 5\ \sum x &= 18 + 15 + 12 + 13 + 12 = 70\ \bar{x} &= \frac{70}{5} = 14 \end{aligned} $$ ## Calculate the sample standard deviation Using the *Sample Standard Deviation* knowledge point $$ \begin{aligned} \sum (x - \bar{x})^2 &= (18-14)^2 + (15-14)^2 + (12-14)^2 + (13-14)^2 + (12-14)^2\ &= 4^2 + 1^2 + (-2)^2 + (-1)^2 + (-2)^2\ &= 16 + 1 + 4 + 1 + 4 = 26\ s &= \sqrt{\frac{26}{5-1}} = \sqrt{\frac{26}{4}} = \sqrt{6.5} \approx 2.55 \end{aligned} $$ The mean is $\bar{x} =$ 14 and the standard deviation is $s =$ 2.55. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Sample Standard Deviation" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the sample mean

Calculate the sample standard deviation

Answer: