Use the following data set to answer the questions.

Question

12,11,16,18,20,21,28,34,19,16,14,17,12,12,18,14,

17,19,21,24,25,13,16

what is the lower extreme?

what is the upper extreme?

what is the lower quartile?

what is the upper quartile?

what is the mean absolute deviation?

what is the standard deviation?

if you have a value of 20 what is the z score?

if the z score of an original value is -1.75 what is the original value

Answer 1

The first thing you need to do, is put the numbers in order from smallest to largest.You can easily answer the first 2 questions: the lower extreme is the small number in the dataset, the upper extreme is the largest number in the dataset.

Now find the median (point that cuts the ordered dates in half, also called the 2nd quartile), now you can easily answer the next 2 questions:the lower quartile is the is the median of the lower half of the data, the upper quartile is the median of the upper half of the data.

The next two are a bit more labor intensive, but here are the formulas to calculate then:

Mean Absolute Deviation: start by finding the mean of the data set. Then find the sum of the data values, and divide the sum by the number of data values. Find the absolute value of the difference between each data value and the mean: | data value – mean |.

Standard Deviation: take the mean(you already have),then for each number subtract the Mean and square the result:(data point-mean)², then find the mean of those squared differences, and finally, take the square root of that number.

For the last 2 questions:

Here's the formula for a z-test z=(x-mu). where x=sample average, mu=population mean, and s=standard deviation s

Since a Z-test is used to test the mean of a distribution, I'm going to assume that '20' is the value for ‘x’, plug in the numbers you’ve already calculated in the equations above and solve to get the value for z, also know as the z-score.

For the last question, they give you the value to plug in the equation for ‘z’, so again, put in the numbers you know, this time you’re solving for ‘x’.

Now, all you have to do are the actual calculations, and you’ll have the answers for then last 2 questions & we’re done!!