Calculate the mode, median and standard deviation for the following values of x: 18, 3, 5, 4, 6, 4, 2, 7.

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william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

You should stick to asking one question per question. So I'm going to answer only the first one you have asked here and have removed the rest.

Now the values we have are : 18, 3, 5, 4, 6, 4, 2, 7

The mode is the value that has the largest number of observations. We can see that the number 4 has two observations, all the others have one. So the mode is 4.

To find the median you have to arrange all the values in increasing or decreasing order and see which is the value that is separating the lower and the higher halves.

So we have 2 , 3, 4, 4, 5, 6, 7, 18. As there are an even number of observations here we find the average of the values at the middle. So the median is (4 +5) /= 4.5

To find the standard deviation, first find the average:

(2+3+4+4+5+6+7+18) / 8 = 6.125

Now find the average of the square of the difference of each term with the average:

[(2 - 6.125)^2  + (3 - 6.125)^2  +(4 - 6.125)^2  +(4 - 6.125)^2  +(5 - 6.125)^2  +(6 - 6.125)^2  +(7 - 6.125)^2  +(18 - 6.125)^2]/8 = 25.55

This is the variance. The square root of the variance is called the standard deviation. Here it is equal to : 5.055

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

x: 18, 3, 5, 4, 6, 4, 2, 7

 2 , 3, 4, 4, 5, 6, 7, 18  the amount of numbers are even therefore we have 2 median numbers.

The numbers are 4 and 5 to find the median we have to add them and divide by 2

4 + 5 = 9 / 3 = 4.5

The median is 4.5

Mode is the number that appears the most, so the mode will be 4

You find the Standard deviation by figuring out the mean (add all the numbers, and divide by how many there are in the set) and subtracting it from every number, then squaring the numbers you got when you subtracted the mean and dividing all the numbers by how many numbers there are in the set. Then find the squareroot of the specific number, you will end up with 5.055

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