Identify the two most commonly used measures of center for quantitative data. Explain the relative advantages and disadvantages of each.

cistG
2020-11-09
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Raheem Donnelly

Answered 2020-11-10
Author has **75** answers

Step 1

Advantages and disadvantages of mean:

Mean is an important measure of centre when the data is quantitative. Mean of a data set is the sum of the data set divided by the size.

Step 2

It is a good measure, since it contains all the data and represent the exact centre of the data. But it will get highly influenced by the outliers in the data. So, the mean is not a good measure if the data contain outliers.

When a data is qualitative one cannot add and divide those data values. So, the mean is not an appropriate measure of centre when the data set is qualitative.

Advantages and disadvantages of median:

Median of a data set is the middle value of the data when the data is arranged in ascending order. Since median considers only the position, not the data values, it won’t be influenced by the outliers. So, the median is the appropriate measure of central tendency when outliers are present.

When the data is qualitative, it is not possible to define an order for that data set. So, the median is not an appropriate measure when data set is qualitative.

Advantages and disadvantages of mean:

Mean is an important measure of centre when the data is quantitative. Mean of a data set is the sum of the data set divided by the size.

Step 2

It is a good measure, since it contains all the data and represent the exact centre of the data. But it will get highly influenced by the outliers in the data. So, the mean is not a good measure if the data contain outliers.

When a data is qualitative one cannot add and divide those data values. So, the mean is not an appropriate measure of centre when the data set is qualitative.

Advantages and disadvantages of median:

Median of a data set is the middle value of the data when the data is arranged in ascending order. Since median considers only the position, not the data values, it won’t be influenced by the outliers. So, the median is the appropriate measure of central tendency when outliers are present.

When the data is qualitative, it is not possible to define an order for that data set. So, the median is not an appropriate measure when data set is qualitative.

asked 2020-11-02

A population of values has a normal distribution with $\mu =49$ and $\sigma =79.5$ . You intend to draw a random sample of size $n=84$ .

Find the probability that a single randomly selected value is greater than 72.4.

$P\left(X>72.4\right)=$ ?

Write your answers as numbers accurate to 4 decimal places.

Find the probability that a single randomly selected value is greater than 72.4.

Write your answers as numbers accurate to 4 decimal places.

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In various applications where we are dealing with electromagnetic or acoustic waves, such as medical imaging, we use the space ${L}^{2}$ or the related Sobolev space ${W}^{1,2}$. I have never seen a reason given for this. Does anyone know why these spaces are preferred over say ${L}^{1}$ spaces?

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What are your suggestions on performing a qui-square test? Mention when you have to perform qui- square Goodness of fit test. Also mention when you have to perform a qui-square Independence Test. Mention the conditions that must be met in order to perform both tests.

asked 2022-06-14

How is finite energy spread wholly in the infinite universe

We all know that energy is never lost, but it transforms into another form.

Doesn't that mean that energy is not unlimited? I mean, why is it that way if it was infinite?

However, if energy is spread throughout the whole world, how can something finite fully fill something infinite?

Does that mean that energy isn't finite? Or the universe isn't infinite? Or maybe there are places without any energy at all?

Of course, there is probably something stupid I'm missing, but an answer would hopefully fix that.

Note: sorry if it's a dumb question, I just heard of it and wasn't able to answer it, nor find it on the web.

We all know that energy is never lost, but it transforms into another form.

Doesn't that mean that energy is not unlimited? I mean, why is it that way if it was infinite?

However, if energy is spread throughout the whole world, how can something finite fully fill something infinite?

Does that mean that energy isn't finite? Or the universe isn't infinite? Or maybe there are places without any energy at all?

Of course, there is probably something stupid I'm missing, but an answer would hopefully fix that.

Note: sorry if it's a dumb question, I just heard of it and wasn't able to answer it, nor find it on the web.

asked 2022-03-04

A chi-square test for independence is being used to evaluate the relationship between two variables, one of which is classified into 2 categories and the second of which is classified into 4 categories. What is the df value for the chi-square statistic?

a. df = 2

b. df = 6

c. df = 7

d. df = 3

a. df = 2

b. df = 6

c. df = 7

d. df = 3

asked 2021-08-10

Use the confidence interval to find the margin of error and the sample mean.

(0.142, 0.300)

The margin of error is ?.

The sample mean is ?.

(0.142, 0.300)

The margin of error is ?.

The sample mean is ?.

asked 2021-08-06

The probability density function of X is $f\left(x\right)=\frac{1}{10}$ for $0\le x\le 10$ . Then $P(X+\frac{10}{X}\ge 7)$ is: