1st year stats, empirical rule- range of values

[m0286]

Hello
I am taking 1st year stats at university, and I have lab questions I am supposed to answer. I am VERY confused.
My data set is:
53, 33, 25, 63,26, 64, 32, 21, 45, 64, 38
I calculated the mean:42.182
the sample variance:272.147
The range:43
The percentile rank of the data value 45: 59th
The value corresponding to the 80th percentile:63
Q1:26
Q2:38
Q3:63
Outliers: none
Standard deviation: 16.497
Now I am asked: according to the empirical rule, if the above data is normal find the range of values in which approximately 68% of the data will lie. I know the empirical rule applies only to bellcurved graphs... but this would not produce a bell curve correct? So would there be an answer?

Then they ask: What is the actual percentage of the data that lie in your interval from above.?

Any help is appreciated thanks!

 

[0rthodontist]

You should know that if the data is normal then about 68% of the data lies within 1 standard deviation of the mean. They expect an incorrect answer for the first part--they are saying, what if it were normal, then what would the answer be.

 

[m0286]

THANKS! I realize now what they are asking and got the answer:

mean-standard deviation=25.685
mean+standard deviation= 58.679

So for the next part: What is the actual percentage of the data that lies in the intervals from previous question.

So would I do, which of these intervals: 22 25 26 32 33 38 45 53 63 64 64 will lie between 25.685 and 58.679??
which is 26, 32, 33, 38, 45, 53
so: 6/11 fall within those intervals, so 6/11 * 100 = 54.54% of the data lie between these intervals.
THANKS again.

 

[0rthodontist]

Yes, that's correct.