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3 years ago

What is the value of the 30th percentile for the data set? 6283 5700 6381 6274 5700 5896 5972 6075 5993 5581 5972 6274 6075 5896

Mathematics

1 answer:

Alex17521 [72]3 years ago

8 0

<h2>Answer:</h2>

5896

<h2>Step-by-step explanation:</h2>

Given data set:

6283 5700 6381 6274 5700 5896 5972 6075 5993 5581 5972 6274 6075 5896

To calculate the 30th percentile;

<em>i. Rearrange the given data set in ascending order.</em>

5581 5700 5700 5896 5896 5972 5972 5993 6075 6075 6274 6274 6283 6381

<em>ii. Use the following formula to get the index of the value at the 30th percentile.</em>

N = p(n)

<em>Where;</em>

N = the number of data points at or below the intended percentile.

p = the intended percentile.

n = the number of points in the data.

p = 30 percent = 0.3

n = 14

<em>Substitute these values into the equation;</em>

N = 0.3(14)

N = 4.2

<em>iii. From the calculated index, find the value of the 30th percentile.</em>

If the index is a whole number x, the desired percentile is the average of the values at index x and x+1.

For example if the index is 4, then the desired percentile is the average of the values at index 4 and 5. In our case, that will be;

$\frac{5896+5896}{2}$ = 5896

If the index is a decimal number, it is rounded up to the nearest integer. The value at the rounded index is the desired percentile.

For example, in our case, the index is 4.2 which when rounded up becomes 4.

Therefore, the data point or value at index 4 is the 30th percentile. From the arrangement in (ii) above, that will be 5896. i.e

5581 5700 5700 <u>5896</u> 5896 5972 5972 5993 6075 6075 6274 6274 6283 6381

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Read 2 more answers

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Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction of normal Variables:

When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

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This means that:

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