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shutvik [7]
3 years ago
14

How to find the first and third quartiles

Mathematics
2 answers:
svet-max [94.6K]3 years ago
4 0
I'll give you an example:
Find the first and third quartiles using this set of data - 3, 5, 7, 8, 9, 11, 15, 16, 20, 21.

Step 1: Put the numbers in order.
3, 5, 7, 8, 9, 11, 15, 16, 20, 21.
Step 2: Make a mark in the center of the data:
3, 5, 7, 8, 9, | 11, 15, 16, 20, 21.
Step 3: Place parentheses around the numbers above and below the mark you made in Step 2–it makes Q1 and Q3 easier to spot.
(3, 5, 7, 8, 9), | (11, 15, 16, 20, 21).
Step 4: Find Q1 and Q3
Q1 is the median (the middle) of the lower half of the data, and Q3 is the median (the middle) of the upper half of the data.
(3, 5, 7, 8, 9), | (11, 15, 16, 20, 21). Q1 = 7 and Q3 = 16.
klio [65]3 years ago
4 0
The first quartile, denoted by Q1 , is the median of the lower half of the data set. This means that about 25% of the numbers in the data set lie below Q1 and about 75% lie above Q1 .The third quartile, denoted by Q3 , is the median of the upper half of the data set. This means that about 75% of the numbers in the data set lie below Q3 and about 25% lie above Q3 
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UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

For this problem, we have that:

We dont know the true proportion, so we use \pi = 0.5, which is when we are are going to need the largest sample size.

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}

0.04\sqrt{n} = 1.96*0.5

\sqrt{n} = \frac{1.96*0.5}{0.04}

(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2

n = 600.25

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}

0.02\sqrt{n} = 1.96*0.5

\sqrt{n} = \frac{1.96*0.5}{0.02}

(\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2

n = 2401

The minimum sample size is 2401.

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3 years ago
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Kipish [7]

Answer:

A is the correct answer

Step-by-step explanation:

To get the fastest answer for these kind of questions, you just have to apply (0, -2) into either one of the 2 equations:

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0 - (-12) =12

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In Candyland, distance is measured in "lollygam" and "gumbo." Suppose there are 8.5 lollygam in a gumbo. Determine the number of
Alik [6]

Answer:

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Step-by-step explanation:

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To know the number of gumbo squared in 110 lollygam squared, we need to know the relation between 1 gumbo squared and 1 lollygam squared, and we do that making the square of our relation between gumbo and lollygams:

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1 gumbo squared -> (8.5)^2 lollygams squared = 72.25 lollygams squared

Now, to know the number of gumbo squared in 110 lollygam squared, we just need to divide 110 by 72.25:

1 gumbo squared -> 72.25 lollygams squared

x gumbo squared -> 110 lollygams squared

x = 110/72.25 =  1.5225 gumbo squared

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