Question

what is the variance of the first 10 numbers of the Fibonacci sequence {0,1,1,2,3,5,8,13,21,34} ?

Answer 1

Step-by-step explanation:

$❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤$

Answer 2

Answer:

The variance of the first $10$ numbers of the Fibonacci sequence is $109.56$.

Step-by-step explanation:

The first $10$ terms of the Fibonacci sequence are : $0,1,1,2,3,5,8,13,21,34$

Steps to find variance:

First, find the arithmetic mean of the given terms.

Mean $=\frac{0+1+1+2+3+5+8+13+21+34}{10}$

$=8.8$

Now, find the square of the deviation of each term from the previously found arithmetic mean.

$(0-8.8)^2=77.44\\(1-8.8)^2=60.84\\(1-8.8)^2=60.84\\(2-8.8)^2=46.24\\(3-8.8)^2=33.64\\(5-8.8)^2=14.44\\(8-8.8)^2=0.64\\(13-8.8)^2=17.64\\(21-8.8)^2=148.84\\(34-8.8)^2=635.04$

Find the mean of the above given values.

This mean is the variance of the given values.

Variance $=\frac{77.44+60.84+60.84+46.24+33.64+14.44+0.64+17.64+148.84+635.04}{10}$

Variance $\\=109.56$

Variance:

The statistical assessment of the variation in numbers within a data collection is known as variance.

In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other.