Statistic Problems With Quartiles and Standard Deviations

Click For Summary
SUMMARY

This discussion focuses on calculating the percentage of data within one, two, and three standard deviations from the mean in a dataset of lactic acid concentrations in cheddar cheese. The mean is 1.44, the median is 1.45, and the standard deviation is 0.3035. The user struggles with determining the correct percentage of data within one standard deviation, mistakenly calculating it as 12% instead of the expected 68%. Additionally, the discussion addresses the relationship between quartiles and standard deviations in a normal distribution, specifically referencing human pregnancy lengths with a mean of 266 days and a standard deviation of 16 days.

PREREQUISITES
  • Understanding of basic statistics concepts such as mean, median, and standard deviation.
  • Familiarity with z-scores and their application in normal distributions.
  • Knowledge of quartiles and their significance in statistical analysis.
  • Ability to interpret data from sample sets, specifically in the context of lactic acid concentrations.
NEXT STEPS
  • Learn how to calculate percentages of data within standard deviations using the empirical rule.
  • Study the calculation of z-scores and their interpretation in statistical contexts.
  • Explore the concept of quartiles and their relationship to standard deviations in normal distributions.
  • Investigate the statistical properties of human pregnancy lengths and their distribution characteristics.
USEFUL FOR

Students, educators, and professionals in statistics, data analysis, and research fields who require a deeper understanding of standard deviations, z-scores, and quartiles in data interpretation.

Rawr
Messages
15
Reaction score
0
There are two different problems that I am confused with:

1) The taste of mature cheese is related to the concentration of lactic acid in cheese. Use the concentrations of lactic acid in 30 samples of cheddar cheese on page 15.

Well, what's important is that using all the numbers it gave me, the mean is 1.44, the median is 1.45 and the standard deviation is .3035.

Then it asks, "Calculate the percent of data that lie within one, two and three standard deviations. I attempted to work with one standard deviation, but I can't seem to get the right answer, which is 66% (or something close).

What I did was... one standard deviation is 1.45 +/- .3035, which gets 1.15 and 1.75. Then you need to calculate the percentage of numbers that fall within that range.

So, I take the z-score of each number: (1.15 - 1.45)/1.44 = -0.21 and it's the same for the other, except it comes out a positive 0.21 using 1.75 instead of 1.15. Using the A chart.. I get numbers of .4168 and .5832 respectively. Subtracting them gives me something like.. 12%. What am I doing wrong? Am I even in the right direction?

The second question..is "How many standard deviations away from the mean do the quartiles lie in any normal distribution? What are the quartile for the lengths of human pregnancies? (which says that... for human pregnancies, the mean is 266 days and the Standard deviation is 16 days)

Frankly, I have no idea how to start and I was hoping I would get a little push in the right direction.
 
Physics news on Phys.org
z_ = 0 - 1 = -1 is the standard z score for "one std below" and z+ = 0 + 1 = +1 is for "one std above."
 

Similar threads

Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 24 ·
Replies
24
Views
7K
Replies
1
Views
3K
  • · Replies 4 ·
Replies
4
Views
5K
  • · Replies 2 ·
Replies
2
Views
5K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K