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3 years ago

Find the mean and standard deviation for the data set

Mathematics

1 answer:

adell [148]3 years ago

6 0

Answer:

See below

Step-by-step explanation:

The mean is simply adding up each data value and dividing your result by the number of data values:

$\text{Mean}=\frac{6+8+7+5+10+6+9+8+4}{9}=\frac{63}{9}=7$

The standard deviation is calculated through finding the sum of the squared differences between the mean and each data point, and dividing that result by the number of data values, which we then take the square root of:

$\text{Standard Deviation}=\sqrt{\frac{(6-7)^2+(8-7)^2+(7-7)^3+(5-7)^2+(10-7)^2+(6-7)^2+(9-7)^2+(8-7)^2+(4-7)^2}{9}}=\sqrt{\frac{10}{3}}\approx1.8257$

What this value means is that each data point is spread about 1.8257 apart from the mean. Standard deviation describes how dispersed the data is in relation to the mean.

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3 years ago

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sleet_krkn [62]

Answer:

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Step-by-step explanation:

Face height=9, bases=6 in

#Assume the pyramid has a square base.

First we need to calculate the perpendicular height of the pyramid:

$#Pythagorean \ Theorem\\a^2+b^2=c^2\\9^2-(0.5\times 6)^2=h^2\\72=h^2\\h=\sqrt{72} \ in$

Now to find the surface area of each pyramid:

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3 years ago

The answer to this problem

Ksivusya [100]

Answer:

B. $\frac{7\sqrt{2}}{34}$

Step-by-step explanation:

Cos θ = Adjacent/hypotenuse

Adjacent = 7

Hypotenuse = √(23² + 7²) = √578 = 17√2

Thus:

Cos θ = $\frac{7}{17\sqrt{2}}$

Rationalize

Cos θ = $\frac{7*\sqrt{2}}{17\sqrt{2}*\sqrt{2}}$

Cos θ = $\frac{7\sqrt{2}}{17*2}$

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3 years ago

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3 years ago

Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morni

Digiron [165]

Answer:

a) The 95% confidence interval for the true mean is:

$8.0695\leq \mu\leq9.2025$

b) This margin of error can be achieved with a sample of size 27 individuals.

Step-by-step explanation:

a) We have to construct a 95% confidence interval for the populations mean WBC.

The sample results, from a sample size n=187, are:

Sample mean: 8.636
Standard deviation: 3.9265

As we are using the sample standard deviation to estimate the population standard deviation, we will use the t-statistic.

The degrees of freedom are:

$df=n-1=187-1=186$

The t-statistic for a 95% interval and 186 degrees of freedom is t=1.9728.

Now, we can calculate the margin of error of the confidence interval:

$E=t \cdot s/\sqrt{n}=1.9728*3.9265/\sqrt{187}=7.7462/13.6748=0.5665$

The upper and lower bound of the confidence interval are:

$LL=\bar x-t \cdot s/\sqrt{n}=8.636-0.5665=8.0695\\\\UL=\bar x+t \cdot s/\sqrt{n}=8.636+0.5665=9.2025$

The 95% confidence interval for the true mean is:

$8.0695\leq \mu\leq9.2025$

b) As the confidence level is equal, the t-value is the same.

But the sample size has to be adjusted to have an margin of error of +/-1.5.

We use the formula for the margin of error:

$E=t \cdot s/\sqrt{n}=1.9728*3.9265/\sqrt{n}=7.7462/\sqrt{n}=1.5\\\\\\n=(\dfrac{7.7462}{1.5})^2=5.1641^2=26.67\approx27$

This margin of error can be achieved with a sample of size 27 individuals.

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3 years ago