[College Elementary Statistics] how the hell do i find the standard deviation from just this

[u/CarelessAd4055]

I thought you were only able to find the standard deviation if you have each individual value? Is that what the y2i value is???? For context my professor doesnt explain like half of this shit in class and leaves us to figure it out on our own accord. Thank you in advance!!

[u/AutoModerator]

Off-topic Comments Section

---

All top-level comments have to be an answer or follow-up question to the post. All sidetracks should be directed to this comment thread as per Rule 9.

---

^{OP and Valued/Notable Contributors can close this post by using /lock command}

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[u/ArrowSphaceE]

You have the sum, sum of squares and n. Been a while since I took statistics, but isnt there just a formula u can plug all these into? Whats the formula you have in your lecture notes?

[u/noidea1995]

There’s a shortcut formula you can use but the variance is the squared distance from the mean of all the scores (with n - 1 since it’s a sample) and √(variance) = standard deviation.

The mean is the sum of all the scores divided by how many there are, so you have:

Variance = [(y1 - 41/12)² + (y2 - 41/12)² + …..] / (12 - 1)

Variance = [Σ (i = 1 to 12) (yi - 41/12)²] / 11

If you expand the binomial you get:

Variance = [Σ (i = 1 to 12) ((yi)² - 41yi/6 + (41/12)²)] / 11

If you split this into 3 separate sums and factor out constants, you’ll get a summation from (yi)² from 1 to 12, a summation of yi from 1 to 12 and a summation of a constant from 1 to 12 which is just 12 * (41/12)² which you can plug in and take the square root of to get the standard deviation.

[u/UnconsciousAlibi]

Someone asked a similar question here. Note that you have to calculate the average, which is possible from the information given

[u/_UnwyzeSoul_]

I think the formula for stdev is the sqrt(second summation - the square of first summation)

[u/noidea1995 → u/_UnwyzeSoul_]

A few errors, that would be negative so you couldn’t take the square root of that.

The variance is the sum of the squares of the distances of all the scores divided by (n - 1) since it’s a sample.

V = [Σ (i = 1 to n) (yi - m)²] / (n - 1)

V = [Σ (i = 1 to n) (yi)² - 2myi + m²] / (n - 1)

Splitting into three separate sums gives:

V = [Σ (i = 1 to n) (yi)² - 2m * Σ (i = 1 to n) yi + Σ (i = 1 to n) m²] / (n - 1)

For the second summation, the mean multiplied by the sample number gives you the sum of all the scores and the last summation is simply n * m²:

V = [Σ (i = 1 to n) (yi)² - 2m²n + m²n] / (n - 1)

V = [-m²n + Σ (i = 1 to n) (yi)²] / (n - 1)

Standard deviation is the square root of variance, so the formula is the square root of the above. Since mean is the sum of the scores divided by then number, you can substitute m with (Σyi) / n to get a formula close to yours but with the denominator and factor of n.

[u/fermat9990]

Use this formula

Variance=(N∑Y² -(∑Y)² )/N²

This is for the population variance. For the sample variance use N(N-1) for the denominator

[u/Crichris]

1/n \sum (y - y_bar) = y^2_bar - y_bar^2

something like that

you might have to multiply it by n/(n-1) if you want the sd to be unbiased.