Z-score introduction | Modeling data distributions | AP Statistics | Khan Academy

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Introducing the idea of a z-score as the number of standard deviations away from the mean a certain data point is.
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[@The_Professor123]

Ah! a classic math video from my main man Mr.Khan

[@BowsSpammed]

Baylen levine refferrnce?

[@shirin8402]

A brain cultivating lecture from an expert, though an effortlessly making math easy mathematician. Brilliant

[@michaeldegraaf3260]

Thanks for the clear explanation, it was so much simpler than I thought

[@adriansegar8392]

Excellent Mr Khan, very good explanation of why the z value is calculated like that . You broken each part down , why is it (X - mean ), then you went through why you divided it by the standard deviation . Excellent

[@NikitaSharma-bs4gg]

It's really fun to learn from Khan Academy....all topics

[@awaizzahid8608]

That’s one class I have been looking for thanks to you sir

[@wellthisisinteresting4912]

FINALLY I GET IT. I was so confused as to what exactly the raw score was. why can't anyone (other than you) just straight up say that its the value of a data point in the data sample we are looking at?? Jesus Christ.

[@alaaadel8900]

اللهم صل على سيدنا محمد وعلى اله وصحبه وسلم تسليما كثيرا عدد خلقك و رضا نفسك وزنة عرشك ومداد كلماتك و عدد ما كان وعدد ما سيكون وعدد الحركات والسكون.

[@xS0G0N3x]

Standard deviation is supposed to be 1.82 isn’t it? n-1? 7-6? Or am I missing something?

[@taylormartin4281]

You are correct. The standard deviation is approx 1.82. 1.83 to be more precise. Good on you for noticing his mistake!

[@TheAce1183]

@@taylormartin4281 He's considering the whole population so you don't need to subtract the 1. it's only if its a sample that you need to subtract a one from

[@Bas1lio]

No. Biased Stdev for those 7 numbers is exactly 1.69. You are talking about unbiased std, but for such small population it leads to significant differences between them, so its better to use biased assessment here.

[@loeysgurlie]

i used this method (1/7) x 20= 2.86 and the square root is 1.69 he is correct :)

[@earlymorningcodes6100]

Very nice for raising such a good concern.I was also doubt ful

[@dillincollins5780]

I think you divided by 'n' instead of (n-1) when calculating variance. The standard deviation should be 1.825.

[@spac3fairy]

That’s what i got too

[@emilyboyle7240]

i keep getting 0 im so confused

[@sm.mehedihasan]

u probably forgot to square @@emilyboyle7240

[@sm.mehedihasan]

yeah

[@samashakti]

oooh, so only if it's a "sample" you do n-1??

[@vincerespecia6473]

How to get the population standard deviation

[@jonataninyumenxibalba935]

does any1 know how to demostrate it?

[@frida5871]

So if I don't have the standard deviation, how do I get it?

[@dashsunil]

Calculate the mean, then substract the mean from each data point, square it, and by sum you willl get the variance. Then divide it by n and take the root. Std. Dev. is the square root of variance. Hope this helps.

[@rudyperez2542]

thank

[@SanAndreasy]

Can someone please explain how did he get the standard deviation? Thanks.

[@444TripleH]

sorry for late reply, but its taking the individual score minus the mean and square it and take the next individual score minus the mean and square it - e.g (2-3)^2 + (2-3)^2.... and then sum up these values and divide by the n and then square it

[@emilyboyle7240]

@@444TripleH u are supposed to divide by n-1 i believe and then find the square root of that

[@444TripleH]

@@emilyboyle7240 oh thanks for correcting if i made a mistake

[@TasyaAdzkiya]

Summary of this video: The reason why the standard deviation is in the denominator is that we want to know how many standard deviation are there in the distance between the value of each of the data point and the population mean. We all know that distance can't be negative but I guess it just for showing us if it's lower than or greater than the population mean. -59/100 of 1.69 is approximately -1. It's not exactly -1 because we round/simplify the 1.69 and the 0.59. I think that the negative is showing us that we have to subtract approximately 59/100 of 1.69 (the standard deviation) from the population mean, which is 3, to get to the value of the first data point, which is 2, and not adding it. We care about this value because it shows us how typical a data point is. The mean is one of the measures that show the typical/average number of all of the data points in a data set, so calculating it will be a great way to measure how typical a data point is based on its distance from the mean (whether it is greater than or less than) and the standard deviation. I think that the reason why we include the standard deviation in the calculation is to show relativity. That is because data sets can have different spread while simultaneously having the same mean, and it just shows us the measure of spread. Just guessing! Please let me know if I make any mistake.

[@sumanchamlingrai9790]

Why do we need z score ?

[@alaaadel8900]

A 10 kg weight loss is expected to decrease blood pressure by 15-20 mmhg Lowering salt intake to 6gm/day can lower systolic blood pressure by 10 mmhg

[@illiteratechild7076]

lol this was made during the algebra 2 regents today

[@emilyboyle7240]

how is the standard deviation 1.69 i keep calculating 0 :0

[@cherazz]

he used the formula σ =√ ∑ (Xi - μ)^2 / N because the turtles make up the entire population. we aren't calculating the SD for a sample so n-1 isn't necessary he did √ (1^2+1^2+1^2+2^2+2^2+3^2) / 7 which gave him 1.69

[@Polo-715]

I think I learn better through videos lmao

[@GrizzlyBear01]

Can't get the 1cm winged turtle out of my head

[@pinkdream3115]

the sum of (xi - the population mean) would be zero though....

[@taylormartin4281]

Sal forgot to subtract 1 from the number of data points, resulting in an incorrect standard deviation of approximately 1.69--√(20÷7). The correct standard deviation is approximately 1.83--√(20÷6).

[@psvishnu1]

Since there are only 7 species of turtles, he might have treated the data points as the whole population. What do you think?

[@seantottenham4367]

@@psvishnu1 you are correct Vishnu PS, at the start of the video Sal explains that the seven turtles are (N) the whole population of that species, not (n) a sample. Therefore, no need to minus 1.

[@sumanchamlingrai9790]

😂😂 wellcome