[Comment on rule of thumb 5 in PRAXIS no. 13]

The range rule of thumb in statistics helps us calculate a dataset's minimum and maximum values with known standard deviation. This rule is based on the concept that 95% of all values in a dataset lie within two standard deviations from the mean.
For instance, the range rule of thumb can be used to find the tallest and the shortest student in a class, given the mean student height and standard deviation. If the mean student height is 1.6 m and the standard deviation, s is 0.05 m, the height of...

The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...

In any measurement, the precision of the measuring tool is an essential factor. An ordinary ruler, for example, can measure length to the closest millimeter; a caliper, on the other hand, can measure length to the nearest 0.01 mm. As a result, the caliper is a more precise measurement tool because it can measure extremely minute changes in length. The measurements will be more accurate if the measuring tool is more precise.
It should be emphasized that when we represent measured values, the...

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...

Estimating the distance traveled by a vehicle using its recorded velocity over time is a common problem in physics and engineering. When velocity data is available at discrete time intervals, rather than as a continuous function, numerical integration methods such as the trapezoidal rule are often employed to approximate the total displacement.The trapezoidal rule works by dividing the total time interval into several equal segments. Within each segment, the recorded velocities at the endpoints...

A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...