54; 18; 76; 42; 76; and 46 mean: median: mode:

1 answer:

4 0

To work out the mean, add them all up and divide by however many values there are:

(18+54+42+(76x2)+46) / 6 = 52

To work out the median, order them from largest to smallest or vice versa and find the middlest value.

18, 42, 46, 54, 76 ,76

(46 + 54) / 2 = 50

The mode is the most frequently occurring number, so it would be 76.

Hope I helped!

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In the problem 19.28 - 1.546, first round each number to the nearest tenth. Then subtract.

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what is the solution of sqrt(2x+4)-sqrt(x)=2 A. x = 0 B. x = 0 and x = 16 C. x = 0 and x = –16 D. x = 16 and x = –16

Charra [1.4K]

We want to solve
√(2x+4) - √(x) = 2

Write equation as
√(2x+4) = √x + 2
Square each side.
2x + 4 = x + 4√x + 4
x = 4√x
x - 4√x = 0
√x (√x - 4) = 0

Either
√x = 0 => x = 0
or
√x = 4 => x = 16

Test for extraneous solutions.
When x = 0:
√(2x+4) - √x = 2 (Correct)
When x = 16:
√(2x+4) - √x = √(36) - √(16) = 6 - 4 = 2 (Correct)

A plot of f(x) = √(2x+4) - √x - 2 = 0 confirms hat the solutions are correct.

Answer: B. x = 0 and x = 16.

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An unknown data set has a standard deviation of 10. What is the standard deviation when each value in the data set is multiplied

solong [7]

Let $\mathbf x=\{x_i~:~1\le i\le n\}$ be the sample, with $n$ the size of the sample.

The mean of the sample is

$\displaystyle\bar x=\frac1n\sum_{i=1}^nx_i$

Let $\mathbf y$ be the same data set but with each value scaled up by 5. Then the mean here is

$\bar y=\displaystyle\frac1n\sum_{i=1}^ny_i=\frac5n\sum_{i=1}^nx_i=5\bar x$

The standard deviation for $\mathbf x$ is given by

$s_{\mathbf x}=\sqrt{\displaystyle\frac1{n-1}\sum_{i=1}^n(\bar x-x_i)^2}$

For $\mathbf y$ , you would have

$s_{\mathbf y}=\sqrt{\displaystyle\frac1{n-1}\sum_{i=1}^n(\bar y-y_i)^2}$
$s_{\mathbf y}=\sqrt{\displaystyle\frac1{n-1}\sum_{i=1}^n(5\bar x-5x_i)^2}$
$s_{\mathbf y}=\sqrt{\displaystyle\frac{25}{n-1}\sum_{i=1}^n(\bar x-x_i)^2}$
$s_{\mathbf y}=5\sqrt{\displaystyle\frac1{n-1}\sum_{i=1}^n(\bar x-x_i)^2}$
$s_{\mathbf y}=5s_{\mathbf x}$