Question

Describe and illustrate (with screenshots within any chosen data analytics/app) the following concepts:

1. Central Tendency,

2. Variability,

3. Normal Distribution,

4. Standardization

Answer 1

Dear student, please comment in the case of any doubt and I would love to clarify it.

Central Tendency

A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset.  These measures indicate where most values in a distribution fall and are also referred to as the central location of a distribution. You can think of it as the tendency of data to cluster around a middle value. In statistics, the three most common measures of central tendency are the mean, median, and mode. Each of these measures calculates the location of the central point using a different method.

Variability

Variability is a measure of the spread of a data set. Learn more about the different measures of variability including the range, variance, and standard deviation, and the way in which they are used in the field of psychology.

The IQR, or the middle fifty, is the range for the middle fifty percent of the data. The IQR only considers middle values, so it is not affected by the outliers.

IQR = Q3 -Q1

Normal Distribution

Early statisticians noticed the same shape coming up over and over again in different distributions—so they named it the normal distribution.

Normal distributions have the following features:

• symmetric bell shape
• mean and median are equal; both located at the center of the distribution
• 68%approximately equals, 68, percent of the data falls within 111 standard deviations of the mean
• 95%approximately equals, 95, percent of the data falls within 222 standard deviations of the mean
• 99.7%approximately equals, 99, point, 7, percent of the data falls within 333 standard deviations of the mean

Standardization

Standardization is the process of putting different variables on the same scale. This process allows you to compare scores between different types of variables. Typically, to standardize variables, you calculate the mean and standard deviation for a variable.

Then, for each observed value of the variable, you subtract the mean and divide by the standard deviation.

This process produces standard scores that represent the number of standard deviations above or below the mean that a specific observation falls. For instance, a standardized value of 2 indicates that the observation falls 2 standard deviations above the mean. This interpretation is true regardless of the type of variable that you standardize.

We use the letter Z to denote it. As we already mentioned, its mean is 0 and its standard deviation is 1.