Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The stardard deviation of lab measurements made by students is sigma=10 milligrams. Juan repeats the measurement 3 times and records the mean xbar of his 3 measurements. (a) What is the standard deviation of Juan's mean result? (That is, if Juan kept making sets of 3 measurements and averaging them, what would be the standard deviation of all his xbar's?) (b) How many times must juan repeat the measurement to reduce the standard deviation of xbar to5? Explain to someone who knows nothing about statistics the advantage of reporting the average of several measurements rather than the result of a single measurement.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
13.6 measurements in the lab.
Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The stardard deviation of lab measurements made by students is sigma=10 milligrams. Juan repeats the measurement 3 times and records the mean xbar of his 3 measurements.
(a) What is the standard deviation of Juan's mean result? (That is, if Juan kept making sets of 3 measurements and averaging them, what would be the standard deviation of all his xbar's?)
(b) How many times must juan repeat the measurement to reduce the standard deviation of xbar to5? Explain to someone who knows nothing about statistics the advantage of reporting the average of several measurements rather than the result of a single measurement.
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