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IrinaVladis [17]
3 years ago
14

Set A of six numbers has a standard deviation of 3 and set B of four numbers has a standard deviation of 5. Both sets of numbers

have an equal mean. If the two sets of numbers are combined, find the variance.​
Mathematics
1 answer:
Alenkinab [10]3 years ago
7 0

Given:

\sigma_A=3

n_A=6

\sigma_B=5

n_B=4

\overline{x}_A=\overline{x}_B

To find:

The variance. of combined set.

Solution:

Formula for variance is

\sigma^2=\dfrac{\sum (x_i-\overline{x})^2}{n}      ...(i)

Using (i), we get

\sigma_A^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{n_A}

(3)^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{6}

9=\dfrac{\sum (x_i-\overline{x}_A)^2}{6}

54=\sum (x_i-\overline{x}_A)^2

Similarly,

\sigma_B^2=\dfrac{\sum (x_i-\overline{x}_B)^2}{n_B}

(5)^2=\dfrac{\sum (x_i-\overline{x}_B)^2}{4}

25=\dfrac{\sum (x_i-\overline{x}_B)^2}{4}

100=\sum (x_i-\overline{x}_B)^2

Now, after combining both sets, we get

\sigma^2=\dfrac{\sum (x_i-\overline{x}_A)^2+\sum (x_i-\overline{x}_B)^2}{n_A+n_B}

\sigma^2=\dfrac{54+100}{6+4}

\sigma^2=\dfrac{154}{10}

\sigma^2=15.4

Therefore, the variance of combined set is 15.4.

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6^3+5(8+0.2)= can someone tell me the steps i know its 257 i need the steps
Sav [38]

Step 1 distribute the 5 across (8+0.2)

6^3+5(8+0.2)

6^3+40+1

6^3+41 (<em>I simplified the +40 and the +1</em>)

Step 2 take 6 to the power of 3

6^3+41

6x6x6     6x6=36     36x6=216

216+41 (<em>Simplify!</em>)

257


I hope this helped!

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Answer:

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Step-by-step explanation:

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Which equation is true for the value x = 15?
boyakko [2]
The third one because 2(15+5)=2(20)=40
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How many times does 44 go into 6,668??? Plz
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151.54 is the answer
The 54 is underlined hence they repeat(use a calculator and you'll see).
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Marcus wants to use the Distributive Property to rewrite 28+72. Which expression could he use?
alexandr1967 [171]

28+72 put into distributive property is 4(7+18)

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Read 2 more answers
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