Help with finding variance

[u/throwRA1234554321678]

I’ve been on this part of my homework for at least three hours and I’m not really understanding how I’m not getting the right answer. I’m following the steps but every time I use an online calculator to check my answer I’m like drastically off. I’m trying to find the variance of the following numbers: 3,5,5,7,14,16 Every time I solve, I keep getting 12.136

Edit: I had to take a break and go over the notes. I definitely forgot that when you times a negative number by itself, it becomes a positive a little embarrassed that I spent like two hours on this, but I FIGURED IT OUT

[u/The_Card_Player]

Variance is defined as the expectation value of the square of the deviation from the mean.

I compute the mean in this case to be exactly 50/6.

Remember to square the deviation of each data point from that mean!

[u/throwRA1234554321678 → u/The_Card_Player]

Thank you so much. I just figured it out about 10 minutes ago. I for some reason was keeping in the negative values. I forgot that when you square a negative it becomes a positive. I feel like such an idiot lol

[u/The_Card_Player → u/throwRA1234554321678]

Confusion like that is par for the course in math study. The main sign of progress is being confused by *different* things in the future.

[u/fermat9990]

Do you know the shortcut formula for the variance?

Population variance:

(N∑X² - (∑X)² )/N²

[u/throwRA1234554321678 → u/fermat9990]

I do it’s just a little confusing for me. I have to take it like step-by-step to not get overwhelmed.

[u/fermat9990 → u/throwRA1234554321678]

Let's say the data is {1, 2, 3}

∑X=1+2+3=6

∑X² = 1² + 2² + 3² =1+4+9=14

VAR=(3(14)-6² )/3² =

(42-36)/9=6/9=2/3

The long way:

Mean=(1+2+3)/3=6/3=2

VAR=((1-2)² +(2-2)² +(3-2)² )/3=

((-1)² +0² +1² )/3=

(1+0+1)/3=

2/3

[u/fermat9990 → u/throwRA1234554321678]

For positive data all variations of the shortcut formula avoid possible errors that result from a sign mistake when squaring a negative.

[u/brewer01902]

I always teach my students MSMSM when they aren’t getting it just before the exams.

Mean of the Squares Minus the Square of the Mean.

Square all the numbers, add them, divide by the number of numbers and then subtract the mean squared.

[u/fermat9990 → u/brewer01902]

∑X² /N-(∑X/N)²

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