# z value

• September 26th 2005, 01:44 PM
lynne smith
statistics
Here is my problem:

Recently you ran a large study over 200,000 data points and came up with a mean,median, and standard deviation.
mean= 345
median= 340
standard deviation =45
would you consider the data to br normally distributed?

3(345-340) /45
3(5) /45=
15/45=
.333
because the data falls between -3 and positive 0.3 the data is normal.

Please let me know if i need to make any corrections.Thank you, Lynne
• September 27th 2005, 04:01 PM
hpe
Quote:

Originally Posted by lynne smith
Here is my problem:
Recently you ran a large study over 200,000 data points and came up with a mean,median, and standard deviation.
mean= 345
median= 340
standard deviation =45
would you consider the data to br normally distributed?

If the data were normal, N(345,45), the sampling distribution of the median with 200,000 data points would be approximately normal with mean 345 and st. dev. $1.25 \cdot 45/\sqrt{200,000} \approx 0.125$.So the actual sample median of 340 would have a z-score of -40, extremely unlikely. The data are definitely not normally distributed.