QuestionCalculate the third moment of the numbers $2, 3, 4, 5, 6$ .

Studdy Solution

STEP 1

Assumptions1. The set of numbers is $,3,4,5,6$ . The third moment is calculated as the sum of the cubed deviations from the mean, divided by the number of numbers in the set.

STEP 2

First, we need to find the mean of the set of numbers. The mean is calculated as the sum of the numbers divided by the number of numbers.
$Mean = \frac{Sum\, of\, numbers}{Number\, of\, numbers}$

STEP 3

Now, plug in the given values for the sum of the numbers and the number of numbers to calculate the mean.
$Mean = \frac{2+3++5+6}{5}$

STEP 4

Calculate the mean.
$Mean = \frac{2+3+4++6}{} =4$

STEP 5

Now, we need to calculate the cubed deviations from the mean. This is done by subtracting the mean from each number, cubing the result, and then summing these cubed deviations.
$Cubed\, deviations = \sum (Number - Mean)^3$

STEP 6

Now, plug in the given values for each number and the mean to calculate the cubed deviations.
$Cubed\, deviations = (2-4)^3 + (3-4)^3 + (4-4)^3 + (5-4)^3 + (6-4)^3$

STEP 7

Calculate the cubed deviations.
$Cubed\, deviations = (-2)^3 + (-1)^3 +0^3 +1^3 +2^3 = - -1 +0 +1 + =0$

STEP 8

Now that we have the cubed deviations, we can find the third moment. The third moment is calculated as the sum of the cubed deviations divided by the number of numbers.
$Third\, moment = \frac{Cubed\, deviations}{Number\, of\, numbers}$

STEP 9

Plug in the values for the cubed deviations and the number of numbers to calculate the third moment.
$Third\, moment = \frac{}{5}$

STEP 10

Calculate the third moment.
$Third\, moment = \frac{0}{5} =0$ The third moment of the set of numbers $2,3,4,5,6$ is $0$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms