Q&A for How to Calculate Z Scores

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How do I calculate the Z score for a 12 month old child who weighs 7 kg?

Community Answer

You would need to know the mean and standard deviation of weights from a large group of other 12 month old children. A doctor might have this information or you may be able to find it online. Then follow the steps in this article.

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Question

What is the Z score for a pulse rate of 69 beats per minute?

Community Answer

Z score requires historical data. Assuming everyone was equally spread between 60-100 bpm, the average is 80. Sample size is 41 (1 for each value between 60-100, inclusive). Mean is 80, Standard Deviation is 11.98. So then (69 - 80) / 11.98, Z = -0.918. This answer is insignificant though, because you need data to calculate a Z score. Heart rate can be grouped by age, weight, habits, etc.

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Question

How can I find the mean?

Community Answer

Add all the numbers, for example; 23+75+80+260=438. Divide the sum with the number of numbers you added up; in this case here, the numbers 23, 75, 80, and 260. There are four numbers in total, so with the sum (438) divide it by 4. 438/4=109.5.

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Question

Where did you get 7.5 from?

Community Answer

7.5 was chosen from the tree heights in Part 1 - Step 1 to compare to the rest of the data set. It was only chosen as an example for how to find the z-score.

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Question

How do I find the Z score for my salary?

Community Answer

Find out the mean and standard deviation of salary of your organization/state/country (depending upon your research area), and use this formula: z = X - μ / σ.

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Question

What is the percentile Z score for a score that is 1.3 standard deviation below the mean?

Community Answer

[(mean-1.3(st.dev))-mean]/st.dev=z score. Use appropriate z-score table to find the percentile or refer to your calculator's normalCDF.

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Question

What if I am only given a mean of 84 and two z-scores of 0 and 0.8? I can't figure out how to find the data points the z-scores come from. Can anyone at least explain how to solve for the variable of x in this situation?

Community Answer

A value of zero zero score mean the first z score is the average which is 84 which is 0 sigma or in the first sigma. 0 = (x - 84)/sigma 0.8 = (x- mean)/sigma 0.8 = (x - 84)/sigma not on the second

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Question

Can I compare Z-scores obtained from two different data sets even though the distributions are different?

Community Answer

The Z score will simply tell you how far away from the mean you are. It shows performance relative to the average. So if two students score z=+2.1 on their tests, regardless of class average or their actual mark, they both are getting A's.

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Question

I want to ask for a raise at work, and want to see what percentile my pay ranks. The minimum hourly pay is $14.33, median is $19.62, and maximum is $24.90. What percentile is my pay of $16.66?

Community Answer

You are being paid 16.26 % more than the lowest, only receiving 84.9% of the median, and receiving a measly 66.9% of the highest.

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Question

How can I use a Z score to find outlier data from a data set?

Community Answer

Any z-score greater than 3 or less than -3 is considered to be an outlier. This rule of thumb is based on the empirical rule. From this rule we see that almost all of the data (99.7%) should be within three standard deviations from the mean.

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Question

If N = 5, where did the N-1 come from? Why am I subtracting the 1 and where did it come from? What am I missing?

Community Answer

In order to remove the mean from the sample size entirely, as it's already been subtracted half way (step three) - a two stage process.

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