What is the median of the data below?<br><br>
45, 19, 23, 67, 28, 35, 46, 21, 58, 60, 23, 51
VLD [36.1K]
To find the median, you will need to list the data from least to greatest and find the middle number.
19, 21, 23, 23, 28, 35, 45, 46, 51, 58, 60, 67
Cross out a number on both sides until you reach the middle number. In this case, we are left with 2 numbers that are in the middle since there is an even amount of numbers.
When you reach the time where you have two middle numbers, we have to find the average of those two numbers. Our two middle numbers are 35 and 45. Since we have to find the average of those two numbers, we can add them. (35 + 45 = 80). Now, since we have two middle numbers, we have to divide them by 2.
![80 \div 2 = 40](https://tex.z-dn.net/?f=80%20%5Cdiv%202%20%3D%2040)
Answer:
Answer:
x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
is equal to
![x=\frac{-b(+/-)\sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%28%2B%2F-%29%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
in this problem we have
![4x^2 + 2x - 1=0](https://tex.z-dn.net/?f=4x%5E2%20%2B%202x%20-%201%3D0)
so
![a=4](https://tex.z-dn.net/?f=a%3D4)
![b=2](https://tex.z-dn.net/?f=b%3D2)
![c=-1](https://tex.z-dn.net/?f=c%3D-1)
substitute in the formula
![x=\frac{-2(+/-)\sqrt{2^2-4(4)(-1)} }{2(4)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-2%28%2B%2F-%29%5Csqrt%7B2%5E2-4%284%29%28-1%29%7D%20%7D%7B2%284%29%7D)
therefore
x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Answer:
![\frac{16r^3}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B16r%5E3%7D%7B3%7D%20)
Step-by-step explanation:
In this cross sections problem, we can integrate from -r to +r (so that the integral covers the entire base of the solid).
![\int\limits^r_a {2(x^2+r^2 )} \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5Er_a%20%7B2%28x%5E2%2Br%5E2%20%29%7D%20%5C%2C%20dx%20)
The formatting for the integral did not let me put -r on the lower bound, so i replaced it with a, just know that a represents -r here.
Evaluating the integral gives use that it is equal to;
![\frac{16r^3}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B16r%5E3%7D%7B3%7D%20)
Caution: this answer may not meet your needs, but this is the answer I have come up with with the given information.
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Answer:
Test statistic,
(to 3 dp)
Step-by-step explanation:
Deviation, d = x -y
Sample mean for the deviation
![\bar{d} = \frac{\sum x-y}{n}](https://tex.z-dn.net/?f=%5Cbar%7Bd%7D%20%3D%20%5Cfrac%7B%5Csum%20x-y%7D%7Bn%7D)
![\bar{d} = \frac{(28-6) + (31-27)+(20-26)+(25-25)+(28-29)+(27-32)+(33-33)+(35-34)}{8} \\\bar{d} = -0.625](https://tex.z-dn.net/?f=%5Cbar%7Bd%7D%20%3D%20%5Cfrac%7B%2828-6%29%20%2B%20%2831-27%29%2B%2820-26%29%2B%2825-25%29%2B%2828-29%29%2B%2827-32%29%2B%2833-33%29%2B%2835-34%29%7D%7B8%7D%20%5C%5C%5Cbar%7Bd%7D%20%3D%20-0.625)
Standard deviation: ![SD = \sqrt{\frac{\sum d^{2} - n \bar{d}^2}{n-1} }](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum%20d%5E%7B2%7D%20-%20n%20%5Cbar%7Bd%7D%5E2%7D%7Bn-1%7D%20%20%7D)
![\sum d^{2} = (28-26)^2 + (31-27)^2 +(20-26)^2 +(25-25)^2 +(28-29)^2 +(27-32)^2 +(33-33)^2 +(35-34)^2\\\sum d^{2} = 63](https://tex.z-dn.net/?f=%5Csum%20d%5E%7B2%7D%20%20%3D%20%2828-26%29%5E2%20%2B%20%2831-27%29%5E2%20%2B%2820-26%29%5E2%20%2B%2825-25%29%5E2%20%2B%2828-29%29%5E2%20%2B%2827-32%29%5E2%20%2B%2833-33%29%5E2%20%2B%2835-34%29%5E2%5C%5C%5Csum%20d%5E%7B2%7D%20%20%3D%2063)
![SD = \sqrt{\frac{63 - 8 * (-0.625)^2}{8-1} }](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B%5Cfrac%7B63%20-%208%20%2A%20%20%28-0.625%29%5E2%7D%7B8-1%7D%20%20%7D)
SD =2.93
Under the null hypothesis, the formula for the test statistics will be given by:
![t_{s} = \frac{ \bar{d}}{s_{d}/\sqrt{n} } \\t_{s} = \frac{- 0.625}{2.93/\sqrt{8} }](https://tex.z-dn.net/?f=t_%7Bs%7D%20%3D%20%5Cfrac%7B%20%5Cbar%7Bd%7D%7D%7Bs_%7Bd%7D%2F%5Csqrt%7Bn%7D%20%20%7D%20%5C%5Ct_%7Bs%7D%20%3D%20%5Cfrac%7B-%200.625%7D%7B2.93%2F%5Csqrt%7B8%7D%20%20%7D)
![t_{s} = -0.6033](https://tex.z-dn.net/?f=t_%7Bs%7D%20%3D%20-0.6033)