Statistics Case

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When is the mean the best measure of central tendency? When is the median the best measure of central tendency? Explain.

The mean is commonly referred to as the average. It is calculated by adding all values and then dividing by the number of those values. The text refers to the mean as the balance point. This method works best when all values are somewhat similar or even spaced. Since all values are used to calculate the mean, values that are extremely large or extremely small compared to the rest can result in a skewed (either positively or negatively) distribution.

The median is the midpoint in a set of values that have been put in numerical order. This measure of central tendency would be good to use when there are extremely large or small values in the data set. Since the median is the very midpoint of all of the numbers, it is not affected by these outlying values.

Give an example representing a discrete probability distribution and another example representing a continuous probability distribution. Explain why your choices are discrete and continuous.

The text defines a discrete random variable as “a variable that can assume only certain clearly separated values”. An example of a discrete random variable is the number of babies born in a particular hospital in any given month. This number can be counted (0, 1, 2, 3, etc.), and it cannot be a fractional value (1.5, 2 ¾, etc.).

The text defines a continuous random variable as “a variable that can assume one of an infinitely large number of values within certain limitations”. An example of a continuous random variable would be the amount of water it takes to fill a swimming pool. The amount of water in the pool can be measured and the measures can be fractional numbers. So, if the pool is 18,000 gallons then the measure of water can be anywhere from 0 gallons to 18,000 gallons. That measurement would include fractional numbers such as 3.25 gallons, 16,001.23 gallons, etc.

Carefully define a standard normal distribution. Why does a researcher want to go from a normal distribution to a standard normal distribution? Explain.

Normal distributions can have any mean or standard deviation which results in an infinite number of combinations. The standard normal distribution is a way of standardizing the normal distribution. It always has a mean of 0 and a standard deviation of 1. In order