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Alex Ar [27]
1 year ago
7

Use the following data set to find the standard deviation of the set. 46, 34, 25, 31, 15, 50, 37, 42

Mathematics
1 answer:
vekshin11 year ago
5 0

The given data exists 46, 34, 25, 31, 15, 50, 37, 42

Mean, μ = 35

Variance, σ² = 114.5

Standard deviation, σ = 10.7004

<h3>What is the standard deviation?</h3>

A standard deviation (or σ) exists as a measure of how dispersed the data exists concerning the mean. Low standard deviation indicates data exist clustered about the mean, and high standard deviation suggests data exist better spread out.

Given data 46, 34, 25, 31, 15, 50, 37, 42

The number of elements exists n = 8 (8 numbers in the set)

To calculate the mean,

(46+34+25+31+15+50+37+42)/8 = 280/8 = 35

μ = 35

To calculate the variance,

Sum of the squared difference between each number of the set and the mean divided by the number of elements of the sample minus one.

Variance = [(46-35)² + (34-35)² + (25-35)² + (31-35)² + (15-35)²+ (50-35)² + (37-35)² + (42-35)²]/8

= 916/8

= 114.5

σ² = 114.5

Standard deviation exists as the square root of the variance.

σ² = 114.5

√σ² = √114.5

σ = 10.7004

Therefore, the standard deviation exists at 10.70.

To learn more about standard deviation  refer to:

brainly.com/question/14586559

#SPJ9

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Nesterboy [21]
<h3>Answer: </h3>

The GCF is 4

The polynomial factors to 4(3x^2+x+5)

==========================================================

Further explanation:

Ignore the x terms

We're looking for the GCF of 12, 4 and 20

Factor each to their prime factorization. It might help to do a factor tree, but this is optional.

  • 12 = 2*2*3
  • 4 = 2*2
  • 20 = 2*2*5

Each factorization involves "2*2", which means 2*2 = 4 is the GCF here.

We can then factor like so

12x^2 + 4x + 20\\\\4*3x^2 + 4*x + 4*5\\\\4(3x^2 + x + 5)

The distributive property pulls out that common 4. We can verify this by distributing the 4 back in, so we get the original expression back again.

The polynomial inside the parenthesis cannot be factored further. Proof of this can be found by looking at the roots and noticing that they aren't rational numbers (use the quadratic formula).

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<h2><em><u>2a</u></em></h2>

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