Question

How would you use Describing Data: Numerical Measures in your daily routine?

Answer 1

Numerical measures The mean, median, mode, percentiles, range, variance, and standard deviation are the most commonly used numerical measures for quantitative data. The mean, often called the average, is computed by adding all the data values for a variable and dividing the sum by the number of data values.

statisticsit’s important to recognize the different types of data numerical, categorical, and ordinal. Data are the actual pieces of information that you collect through your study. For example, if you ask five of your friends how many pets they own, they might give you the following data 0, 2, 1, 4, 18.

(The fifth friend might count each of her aquarium fish as a separate pet.) Not all data are numbers; let’s say you also record the gender of each of your friends, getting the following data: male, male, female, male, female.

Most data fall into one of two groups: numerical or categorical.

Numerical data. These data have meaning as a measurement, such as a person’s height, weight, IQ, or blood pressure or they’re a count, such as the number of stock shares a person owns, how many teeth a dog has, or how many pages you can read of your favorite book before you fall asleep. (Statisticians also call numerical data or quantitative data.)

Numerical data can be further broken into two types

discrete and continuous.

Discrete data represent items that can be counted; they take on possible values that can be listed out. The list of possible values may be fixed (also called finite); or it may go from 0, 1, 2, on to infinity.

For example, the number of heads in 100 coin flips takes on values from 0 through 100 (finite case), but the number of flips needed to get 100 heads takes on values from 100 (the fastest scenario) on up to infinity (if you never get to that 100th heads). Its possible values are listed as 100, 101, 102, 103, . . . (representing the countably infinite case).

Continuous data represent measurements; their possible values cannot be counted and can only be described using intervals on the real number line. For example, the exact amount of gas purchased at the pump for cars with 20-gallon tanks would be continuous data from 0 gallons to 20 gallons, represented by the interval [0, 20], inclusive. You might pump 8.40 gallons, or 8.41, or 8.414863 gallons, or any possible number from 0 to 20. In this way, continuous data can be thought of as being uncountably infinite. For ease of recordkeeping, statisticians usually pick some point in the number to round off. Another example would be that the lifetime of a C battery can be anywhere from 0 hours to an infinite number of hours (if it lasts forever), technically, with all possible values in between.