Question 1125795: How do I calculate my raw score to find my z score.
My mean is 20.87857143, median is 20, mode is 18, and my standard deviation is 4.185394023.
What z-score would a 40 year-old have? Would it be unusual to have a 40 year-old? (yes right because nobody is 40 years old?) Determine the skew of the data
my data of ages includes:
18,19,20,19,29,20,18
18,18,20,19,23,18,19,18,21
36,24,26,26,20,18,22,18,18
18,19,20,27,21,20,18,20,18
19,27,18,22,18,18,18,19,18
18,19,20,19,18,19,19,31,20
18,22,17,20,38,20,18,21
21,31,24,23,18,19,19,21
19,17,39,21,18,18,18,21
32,33,17,22,19,18,20,29
21,20,24,18,23,21,21,22
18,20,19,18,19,18,18,18
18,22,20,21,18,20,18,17
21,19,25,17,20,18,25,19
22,26,18,23,25,19,18,20
20,19,18,22,23,21,18,18
19,22,20,22,17,27,33,20
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 18,19,20,19,29,20,18,18,18,20,19,23,18,19,18,21,36,24,26,26,20,18,22,18,18,18,19,20,27,21,20,18,20,18,19,27,18,22,18,18,18,19,18,18,19,20,19,18,19,19,31,20,18,22,17,20,38,20,18,21,21,31,24,23,18,19,19,21,19,17,39,21,18,18,18,21,32,33,17,22,19,18,20,29,21,20,24,18,23,21,21,22,18,20,19,18,19,18,18,18,18,22,20,21,18,20,18,17,21,19,25,17,20,18,25,19,22,26,18,23,25,19,18,20,20,19,18,22,23,21,18,18,19,22,20,22,17,27,33,20
i looked at your data in excel.
a 40 year old would have a z-score that would be calculated as follows:
z = (x-m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard error.
the z-core for a 40 year old within this data set (the sample is assumed to be the population), would be:
z = (40 - 20.88) / 4.19 = 4.56.
the probability of getting a z-score greater than 4.56 would effectively be 0.
most z-score tables only go up to about plus or minus 3.4.
from excel, the kurtosis is about 5 and the skewness is about 2.2.
both are out of what is considered normal range, although there are differing opinions as to what is an acceptable range.
some says 2.2 for both.
some say 1 for skewness and 3 for kurtosis.
there are other opinions as well.
here's an example of a discussion.
https://www.researchgate.net/post/What_is_the_acceptable_range_of_skewness_and_kurtosis_for_normal_distribution_of_data
fyi - i'm not a statistician so don't think what i say is from an expert.
it's not.
most of what was said in this discussion is way over my head.
here are the results from excel based on your data set.
here are the results from the z-score calculator by david m. lane.
first the raw score results.
then the z-score results.
the results from the raw score test and the z-score test are consistent, as they should be.
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