In statistics, several tools are used to interpret the data. Measures of central tendency represent the characteristics of the data, such as mean, median, and mode. Additionally, measures of variance like standard deviation and range are used to find the spread of data from the mean. Relative standing measures the distance between data locations. Commonly used measures of relative standings are percentile, z score, and quartiles.
Percentiles are a type of fractile that partition data into...

Data are individual items of information obtained from a population or sample. Data may be classified as qualitative (categorical), quantitative continuous, or quantitative discrete. Because it is not practical to measure the entire population in a study, researchers use samples to represent the population. A random sample is a representative group from the population chosen by using a method that gives each individual in the population an equal chance of being included in the sample. Random...

The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
In hypothesis testing, a sample statistic is converted to a test statistic using z, t, or chi-square distribution. A critical region is an area under the curve in  probability distributions demarcated by the critical value. When the test statistic falls in this region, it suggests that the null hypothesis must be rejected. As this region contains all those values of the...

A critical value is a definite value obtained from a particular probability distribution at a predecided confidence level (or a predecided significance level) for a given population parameter. The critical value provides demarcation that separates the sample statistics that are likely to occur from the ones that are unlikely to occur based on the given probability distribution and the population parameter to be estimated. The critical value for normal distribution is obtained from the z...

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...

Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...