A student is performing measurements in the chemistry laboratory and recording the results in a lab report. The student performs the experiment four times and records the mean x of the four measurement trials. Suppose that the chemistry teacher has found that ? = 12 milligrams from previous similar experiments. (a) What is the standard deviation of the student's mean result? (That is, if the student kept on making four measurements and averaging them, what would be the standard deviation of all the x values?) mg (b) How many times must the student perform the measurement to reduce the standard deviation of x to 2? n = (c) Explain to someone who knows no statistics the advantage of reporting the average of several measurements rather than the result of a single measurement. -The average of several measurements will always be an unbiased estimate of the mean. -The average of several measurements is more likely than a single measurement to be close to the mean. -The result of a single measurement will never be close to the mean. -Taking several measurements reduces the likelihood of reporting error.
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.
A student is performing measurements in the chemistry laboratory and recording the results in a lab report. The student performs the experiment four times and records the
mg
(b) How many times must the student perform the measurement to reduce the standard deviation of x to 2?
(c) Explain to someone who knows no statistics the advantage of reporting the average of several measurements rather than the result of a single measurement.
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