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alex41 [277]
3 years ago
5

Compute the standard deviation for the set of data. 13.3, 14.3, 15.3, 16.3, 17.3

Mathematics
1 answer:
Gennadij [26K]3 years ago
6 0
<h3>Answer: Choice A)  sqrt(2)</h3>

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

Explanation:

Add up all of the values

13.3+14.3+15.3+16.3+17.3 = 76.5

Then divide by 5 as there are n = 5 values in the set given

76.5/5 = 15.3

The mean of this data set is 15.3

-------------

Subtract the mean from each value to get this list of differences

x1 - mean = 13.3 - 15.3 = -2

x2 - mean = 14.3 - 15.3 = -1

x3 - mean = 15.3 - 15.3 = 0

x4 - mean = 16.3 - 15.3 = 1

x5 - mean = 17.3 - 15.3 = 2

-------------

Square each result from the previous section

(-2)^2 = 4

(-1)^2 = 1

(0)^2 = 0

(1)^2 = 1

(2)^2 = 4

Then add up those results

4+1+0+1+4 = 10

This is the sum of the squared differences.

------------

Divide the sum of the squared differences by n = 5 to get 10/5 = 2

The population variance is 2

The population standard deviation is the square root of this, so we get sqrt(2) as our final answer.

------------

Side note: This data set was fairly small, so computing the standard deviation by hand wasnt too painful. When it comes to larger data sets, it is smarter to use a spreadsheet program to easily calculate the answer. The drawback is that you wont be able to get an exact answer in terms of radicals (then again you could always use a CAS, which stands for "computer algebra system").

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Answer:

Option (3)

Step-by-step explanation:

From the picture attached,

Bar graph sketched shows the grades earned by the students in an exam.

Number of students who achieved the grade A = 17

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Number of students with grade C = 5

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Option (1)

"\frac{1}{5} of the students earned a C"

Fraction of students who earned C = \frac{\text{Students who earned C}}{\text{Total students}}

                                                          = \frac{5}{45}

                                                          = \frac{1}{9}

Therefore, this option is incorrect.

Option (2)

"3% more students earned an A then B"

Percentage of students who earned A = \frac{\text{Students got A}}{\text{Total students who took the exam}}\times 100

                                                                = \frac{17}{45}\times 100

                                                                = 37.78%

Percentage of students who earned B = \frac{\text{Students got B}}{\text{Total students who took the exam}}\times 100

                                                                = \frac{14}{45}\times 100

                                                                = 31.11%

Difference in percentage = 37.78 - 31.11

                                          = 6.67%

Therefore, this option is not correct.

Option (3)

"20% of the students earned a D"

Percentage of students who earned D = \frac{\text{Students got D}}{\text{Total students who took the exam}}\times 100

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

                                                                 = 20%

Option (3) is the correct option.

Option (4)

" \frac{1}{4} of the class earned a B"

Fraction of class who earned B = \frac{\text{Students got B}}{\text{Total students who took the exam}}

                                                    = \frac{14}{45}

Therefore, Option (4) is not correct.                                        

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