Answer:
<u><em>-29/15</em></u>
Step-by-step explanation:
- <u><em>Multiply 2 and 3 to get 6</em></u>
- <u><em>-6+2/3 + 11/15</em></u>
- <u><em>Add 6 and 2 to get 8</em></u>
- <u><em>-8/3+11/15</em></u>
- <u><em>LCM of 3 and 15 is 15. Convert -8/3 and 11/15 to fractions with 15 as the denominator</em></u>
- <u><em>-40/15 + 11/15</em></u>
- <u><em>Since -40/15 and 11/15 have the same denominator, add them by adding the numerators</em></u>
- <u><em>-40+11 / 15</em></u>
- <u><em>Add -40 snd 11 to get -29</em></u>
- <u><em>-29/15</em></u>
Answer:
<h2>B. 7.1</h2>
Step-by-step explanation:
Given the sample data 2 6 15 9 11 22 1 4 8 19, before we can get the standard deviation, we need to first calculate the mean.
mean = 2 +6 +15 +9 +11 +22 +1 +4 +8 +19/10
mean = 97/10
mean = 9.7
Standard deviation for ungrouped data is expressed using the formula;
![S = \sqrt{ \dfrac{\sum(x-\overline x)^2}{n-1} }](https://tex.z-dn.net/?f=S%20%3D%20%5Csqrt%7B%20%5Cdfrac%7B%5Csum%28x-%5Coverline%20x%29%5E2%7D%7Bn-1%7D%20%7D)
![\overline x \ is\ the \ mean\\n \ is \ sample \ size](https://tex.z-dn.net/?f=%5Coverline%20x%20%5C%20is%5C%20the%20%5C%20mean%5C%5Cn%20%5C%20is%20%5C%20sample%20%5C%20size)
![S = \sqrt{\frac{(2-9.7)^2+(6-9.7)^2+(15-9.7)^2+(9-9.7)^2+(11-9.7)^2+(22-9.7)^2+(1-9.7)^2+(4-9.7)^2+(8-9.7)^2+(19-9.7)^2}{10-1} }\\ S = \sqrt{\frac{(-7.7)^2+(-3.7)^2+(5.3)^2+(-0.7)^2+(1.3)^2+(12.3)^2+(-8.7)^2+(-5.7)^2+(-1.7)^2+(9.3)^2}{10-1} }\\\\S = \sqrt{\dfrac{59.29+13.69+28.09+0.49+1.69+151.29+75.69+32.49+2.89+86.49}{10-1} }\\\\\\S = \sqrt{\dfrac{452.1}{9} }\\\\S = \sqrt{50.23}\\ \\S = 7.08\\\\S \approx 7.1](https://tex.z-dn.net/?f=S%20%3D%20%5Csqrt%7B%5Cfrac%7B%282-9.7%29%5E2%2B%286-9.7%29%5E2%2B%2815-9.7%29%5E2%2B%289-9.7%29%5E2%2B%2811-9.7%29%5E2%2B%2822-9.7%29%5E2%2B%281-9.7%29%5E2%2B%284-9.7%29%5E2%2B%288-9.7%29%5E2%2B%2819-9.7%29%5E2%7D%7B10-1%7D%20%7D%5C%5C%20S%20%3D%20%5Csqrt%7B%5Cfrac%7B%28-7.7%29%5E2%2B%28-3.7%29%5E2%2B%285.3%29%5E2%2B%28-0.7%29%5E2%2B%281.3%29%5E2%2B%2812.3%29%5E2%2B%28-8.7%29%5E2%2B%28-5.7%29%5E2%2B%28-1.7%29%5E2%2B%289.3%29%5E2%7D%7B10-1%7D%20%7D%5C%5C%5C%5CS%20%3D%20%20%5Csqrt%7B%5Cdfrac%7B59.29%2B13.69%2B28.09%2B0.49%2B1.69%2B151.29%2B75.69%2B32.49%2B2.89%2B86.49%7D%7B10-1%7D%20%7D%5C%5C%5C%5C%5C%5CS%20%3D%20%20%5Csqrt%7B%5Cdfrac%7B452.1%7D%7B9%7D%20%7D%5C%5C%5C%5CS%20%3D%20%5Csqrt%7B50.23%7D%5C%5C%20%5C%5CS%20%3D%207.08%5C%5C%5C%5CS%20%5Capprox%207.1)
<em>Hence the standard deviation of the sample data is 7.1</em>
Answer:
-4
Step-by-step explanation: