What Are And How To Calculate Z Scores - Z Score Statistics Formula Explained

In this video we discuss what are z scores and how to calculate z scores using a formula, which uses the mean and standard deviation.
Transcript/notes
Z scores
A z score or standard score for a value is the number of standard deviations that value falls above or below the mean.
Z scores give us a way to compare 2 different variables from different data sets to one another based on where they are located in relation to their individual means.
The formula for the z score is, z = a value minus the mean, divided by the standard deviation. A z score with a positive value is above the mean, a negative value is below the mean, and a z score of zero means it is equal to the mean. On the screen is the formula for both samples and populations.
For an example, let’s say that Karen here is competing for a promotion at work with 100 other people, and recently took a practice exam.
The practice and real exam are based on 3 categories, leadership, quickly processing information and data analysis.
On the practice exam she scored a 22 in leadership, a 12 in info processing, and a 34 in data analysis.
The group results for the practice exam were given to all applicants, for leadership the mean was 18, and standard deviation was 4.8, for info processing, the mean was 9 with a standard deviation of 1.8, and for data analysis, the mean was 32 with a standard deviation of 1.8.
The good thing is is that Karen was above the mean in all 3 categories, but she has 3 weeks to study for the real exam and wants to put most of her study time into her weakest categories.
To find this out, she can calculate her z scores for each of the categories to give her an idea of what she is weakest at, compared to other applicants.
Using the z score formula for leadership, she scored a 22, subtract the mean of 18, and divide that result by 4.8, the standard deviation, which gives us 0.83. For info processing she scored a 12, minus the mean of 9, and divide by a standard deviation of 1.2, and we get 2.5. And for data analysis she got a 34, minus a mean of 32, and divide by a standard deviation of 1.8, and we get 1.11.
Since her z score of 2.5 in info processing is her highest of the 3, her relative position in this category is higher than the other categories, and her z score of 0.83 is lowest in leadership, her relative position in this category is her lowest.
So, based on this data, she should spend most of her study time on leadership, then on data analysis and lastly on info processing techniques.
To make this a little clearer, we can draw a line and mark x bar, the mean, in the middle.
And we can put in 6 other marks, being x bar plus and minus 1, 2, and 3s, where s represents standard deviation. Now we can estimate and draw a line at x bar plus 0.83, which is her z score in leadership, draw another line at x bar plus 1.11, her z score in data analysis, and another line at 2.5, her z score in info processing.
If you think of the right end of the line as being the top ranked applicants hopefully this gives you a visual perspective of her z scores.
Timestamps
0:00 Z Scores Explained/Overview
0:16 Z Score Formula Explained
0:33 Z Score Example Problem
2:01 Z Score Interpretation

[@MillyIrw]

Thank you so much for the help!!! This helped me sooo much, I'm struggling in statistics

[@bilivuk4]

Concise and clear, thank you!

[@keshaaa6568]

OMGGG Thank you very much!💓
Out of all the videos that I have watched, this one really helped me!💓

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I was stupid forgot my account password. I appreciate any tricks you can offer me

[@breezyjayee]

AWESOME VIDEO THANK YOU!!!

[@B-AANKITOJHA]

Great work with video and data sir

[@estrangedfiction7799]

awesome video! it solved my problem thank you!

[@AbAb-mm3og]

'liked'. Thank you for the video.

[@afzaltar2750]

Good video. Short and to the point.

[@whatsupdude2778]

Glad it was helpful! Thanks for watching my friend.

[@sidraasif4667]

Thank you!

[@payojaaa]

GREAT VIDEO!!! thankyou so much!!! it helped me a ton for my stat test that is today!

[@anhvuucanh7356]

Darn good sir

[@leenarjah403]

i love u bro, thank you so much

[@user-mi1ns5xc2z]

Thank you😊

[@laxmanbehera3652]

Thanks 👍🙏

[@nevergiveup2198]

This is so good thank u so much
Just wanna ask
My Z score on exam was 0.82
The highest of us was 2.5
The lowest-2.61
And we are 79 students
What is my level?

[@twelvemonths_]

Hands down ❤️

[@mrjrpnls829]

고맙타 ❤

[@luciafernandes7365]

saved me thank u

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OMG I LOVE THUS

[@angiechartier2582]

I use this video to fall asleep. Thank you, Bryan! 😊😊 Angie

[@whatsupdude2778]

Well, even if you didn't learn anything from the video, at least it has some sort of value for you, lol.

[@nbeck9188]

What if you don’t have a standard deviation, how do you find it or use it?

[@Ok-bb8bi]

How did you find the mean and sd

[@scott9628]

So, this is what Chandler Bing does!

[@atarahtumlos2024]

How did you find the mean and the standard deviation?

[@tdhb8025]

Umm sir how do u get the deviation?

[@alenatilikenova7056]

there are a lot of z scores in statistics.I dont understand which kind of you explained? please let me know

[@taniquejackson538]

what is the z-score for prison time served of 79.5 months

[@georgebox100]

what is my z-score ? _______
t-score is left neck is -3.1
....right neck is t-score -3.3....
spine t-score -4.4.....
my age is 53 male, 5.4 height for osteoporosis

[@TheDroidMate]

You're not giving any hint towards the standard error

[@DogesMemeFactory]

Did not help

[@runningman7162]

Use this as a "Lets Go Buffalo!" Button

[@michellegvrcia]

Thank you!