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What is the arithmetic mean of the following numbers?
1,2, 10, 6, 4,4,6,3,1,4

User Sger
by
8.7k points

1 Answer

1 vote

Answer:

The quadratic mean (rms) of a set of numbers is the square root of the sum of the squares of the numbers divided by the number of terms.

(

1

)

2

+

(

2

)

2

+

(

10

)

2

+

(

6

)

2

+

(

4

)

2

+

(

4

)

2

+

(

6

)

2

+

(

3

)

2

+

(

1

)

2

+

(

4

)

2

10

Explanation:

One to any power is one.

1

+

(

2

)

2

+

(

10

)

2

+

(

6

)

2

+

(

4

)

2

+

(

4

)

2

+

(

6

)

2

+

(

3

)

2

+

(

1

)

2

+

(

4

)

2

10

Raise

2

to the power of

2

.

1

+

4

+

(

10

)

2

+

(

6

)

2

+

(

4

)

2

+

(

4

)

2

+

(

6

)

2

+

(

3

)

2

+

(

1

)

2

+

(

4

)

2

10

Raise

10

to the power of

2

.

1

+

4

+

100

+

(

6

)

2

+

(

4

)

2

+

(

4

)

2

+

(

6

)

2

+

(

3

)

2

+

(

1

)

2

+

(

4

)

2

10

Raise

6

to the power of

2

.

1

+

4

+

100

+

36

+

(

4

)

2

+

(

4

)

2

+

(

6

)

2

+

(

3

)

2

+

(

1

)

2

+

(

4

)

2

10

Raise

4

to the power of

2

.

1

+

4

+

100

+

36

+

16

+

(

4

)

2

+

(

6

)

2

+

(

3

)

2

+

(

1

)

2

+

(

4

)

2

10

Raise

4

to the power of

2

.

1

+

4

+

100

+

36

+

16

+

16

+

(

6

)

2

+

(

3

)

2

+

(

1

)

2

+

(

4

)

2

10

Raise

6

to the power of

2

.

1

+

4

+

100

+

36

+

16

+

16

+

36

+

(

3

)

2

+

(

1

)

2

+

(

4

)

2

10

Raise

3

to the power of

2

.

1

+

4

+

100

+

36

+

16

+

16

+

36

+

9

+

(

1

)

2

+

(

4

)

2

10

One to any power is one.

1

+

4

+

100

+

36

+

16

+

16

+

36

+

9

+

1

+

(

4

)

2

10

Raise

4

to the power of

2

.

1

+

4

+

100

+

36

+

16

+

16

+

36

+

9

+

1

+

16

10

Add

1

and

4

.

5

+

100

+

36

+

16

+

16

+

36

+

9

+

1

+

16

10

Add

5

and

100

.

105

+

36

+

16

+

16

+

36

+

9

+

1

+

16

10

Add

105

and

36

.

141

+

16

+

16

+

36

+

9

+

1

+

16

10

Add

141

and

16

.

157

+

16

+

36

+

9

+

1

+

16

10

Add

157

and

16

.

173

+

36

+

9

+

1

+

16

10

Add

173

and

36

.

209

+

9

+

1

+

16

10

Add

209

and

9

.

218

+

1

+

16

10

Add

218

and

1

.

219

+

16

10

Add

219

and

16

.

235

10

Cancel the common factor of

235

and

10

.

Tap for fewer steps...

Factor

5

out of

235

.

5

(

47

)

10

Cancel the common factors.

Tap for fewer steps...

Factor

5

out of

10

.

5

47

5

2

Cancel the common factor.

5

47

5

2

Rewrite the expression.

47

2

Rewrite

47

2

as

47

2

.

47

2

Multiply

47

2

by

2

2

.

47

2

2

2

Combine and simplify the denominator.

Tap for fewer steps...

Multiply

47

2

and

2

2

.

47

2

2

2

Raise

2

to the power of

1

.

47

2

2

1

2

Raise

2

to the power of

1

.

47

2

2

1

2

1

Use the power rule

a

m

a

n

=

a

m

+

n

to combine exponents.

47

2

2

1

+

1

Add

1

and

1

.

47

2

2

2

Rewrite

2

2

as

2

.

Tap for fewer steps...

Use

n

a

x

=

a

x

n

to rewrite

2

as

2

1

2

.

47

2

(

2

1

2

)

2

Apply the power rule and multiply exponents,

(

a

m

)

n

=

a

m

n

.

47

2

2

1

2

2

Combine

1

2

and

2

.

47

2

2

2

2

Cancel the common factor of

2

.

Tap for more steps...

47

2

2

1

Evaluate the exponent.

47

2

2

Simplify the numerator.

Tap for fewer steps...

Combine using the product rule for radicals.

47

2

2

Multiply

47

by

2

.

94

2

The result can be shown in multiple forms.

Exact Form:

94

2

Decimal Form:

4.84767985

User Fleshgolem
by
8.2k points

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