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Arisa [49]
3 years ago
12

Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. He finds the mean is 14. His steps for

finding the standard deviation are below. What is the first error he made in computing the standard deviation?
A. Yuri failed to find the difference between each data point and the mean.
B. Yuri divided by n instead of n -1.
C. Yuri did not subtract 9 - 14 correctly.
D. Yuri failed to square -2 correctly.

Mathematics
2 answers:
Amiraneli [1.4K]3 years ago
7 0

Answer:

C

Step-by-step explanation:

Well, the first useful step to find the Standard Deviation is to organize it into a table. Let's insert the information. The data set ={9,12,14,21} Mean = 14 n= quantity of observations, in this case: 4

1) In the first column, the data set. In the second column, the squared difference of each number minus the mean. The sum of the second column will be plugged into the ∑ formula. (Check below)

2) Notice that in the second row, where x value is 9. (x-xbar)²= (9-14)². Yuri has made that mistake, and He compromised all the calculations.

KATRIN_1 [288]3 years ago
4 0

Answer:

Option B.

Step-by-step explanation:

Consider the below figure attached with this question.

Formula for standard deviation of a sample:

s=\sqrt{\dfrac{\sum (x-\overline{x})^2}{n-1}}

where, n is sample size and \overline{x} is sample mean.

The sample data set is 12, 14, 9, and 21.

The mean is 14.

So, the sample standard deviation is

s=\sqrt{\dfrac{(12-14)^2+(14-14)^2+(9-14)^2+(21-14)^2}{4-1}}

According to Yuri,

s=\sqrt{\dfrac{(12-14)^2+(14-14)^2+(9-14)^2+(21-14)^2}{4}}

Yuri divides the sum of square of difference between each data point and the mean by n instead of n -1.

Therefore, the correct option is B.

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Answer:

The simplest form of the fraction \frac{45}{100}  is  \frac{9}{20}.

i.e.

\frac{45}{100}=\frac{9}{20}

Step-by-step explanation:

Here are some simple observations regarding how to reduce a fraction into simpler terms:

  • A fraction is reduced to lowest or simplest terms by finding an equivalent fraction in which the numerator and denominator are as small as possible.
  • In order to reduce a fraction to lowest or simplest terms, divide the numerator and denominator by their (GCF). Note that (GCF) is also called Greatest Common Factor .

So, lets take a sample fraction and reduce into simpler terms.

Considering the fraction

\frac{45}{100}

\mathrm{Find\:a\:common\:factor\:of\:}45\mathrm{\:and\:}100\mathrm{\:in\:order\:to\:cancel\:it\:out}

\mathrm{Greatest\:Common\:Divisor\:of\:}45,\:100:\quad 5

\mathrm{Factor\:out\:}5\mathrm{\:from\:the\:numerator\:and\:the\:denominator}

45=5\cdot \:9\mathrm{,\:\quad }100=5\cdot \:20

so

\frac{45}{100}=\frac{5\cdot \:\:9}{5\cdot \:\:20}

\mathrm{Cancel\:the\:common\:factor:}\:5

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Therefore, the simplest form of the fraction \frac{45}{100}  is  \frac{9}{20}.

i.e.

\frac{45}{100}=\frac{9}{20}

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