Descriptive and Inferential Statistics.docx

Descriptive statistics describe, visualize, and summarize the basic characteristics of a data set found in a
particular study, presented in a summary that describes the data sample and its measurements. Help
analysts better understand the data.
Descriptive statistics represent the sample of data available and do not include theories, inferences,
probabilities, or conclusions. This is a work of inferential statistics.
The prime purpose of descriptive statistics is to convey information regarding a data set. It helps in
reducing a large chunk of data into a few relevant pieces of information.
A good example of descriptive statistics, student’s grade point average (GPA). A GPA gathers the data
points created through a large selection of grades, classes, and exams then average them together and
presents a general idea of the student’s mean academic performance. Note that the GPA doesn’t predict
future performance or present any conclusions. Instead, it provides a straightforward summary of
students’ academic success based on values pulled from data.
Here’s an even simpler example. Let’s assume a data set of 2, 3, 4, 5, and 6 equals a sum of 20. The data
set’s mean is 4, arrived at by dividing the sum by the number of values (20 divided by 5 equals 4).
Analysts often use charts and graphs to provide descriptive statistics. If you stand outside a movie
theater and ask 50 people if they liked the movie they saw and put your results in a pie chart, that’s
descriptive statistics. In this example, descriptive statistics measure yes and no responses and show how
many people in that theater liked or disliked the movie. If you try to make other inferences, you run into
inference statistics, but we’ll get to that later.
Descriptive statistics break down into several types, characteristics, or measures. Some authors say that
there are two types. Others say three or even four.
Distribution (Also Called Frequency Distribution)
Datasets consist of a distribution of scores or values. Statisticians use graphs and tables to summarize
the frequency of every possible value of a variable, rendered in percentages or numbers.
Measures of Central Tendency
Measures of central tendency estimate a dataset’s average or center, finding the result using three
methods: mean, mode, and median.
Variability (Also Called Dispersion)
The measure of variability gives the statistician an idea of how spread out the responses are. The spread
has three aspects — range, standard deviation, and variance.
Univariate Descriptive Statistics
Univariate descriptive statistics are helpful when it comes to summarizing huge amounts of numerical
data as well as revealing patterns in the raw data.

Inferential statistics
While descriptive statistics summarize the characteristics of a data set, inferential statistics help you
come to conclusions and make predictions based on your data.
When you have collected data from a sample, you can use inferential statistics to understand the larger
population from which the sample is taken.
Inferential statistics have two main uses:
1. Making estimates about populations (for example, the mean SAT score of all 11th
graders in the
Philippines).
2. Making hypotheses to draw conclusions about populations (for example, the relationship
between SAT scores and family income).
With inferential statistics, it’s important to use random and unbiased sampling methods. If your sample
isn’t representative of your population, then you can’t make valid statistical inferences or generalize.
Since the size of a sample is always smaller than the size of the population, some of the population isn’t
captured by sample data. This creates sampling error, which is the difference between the true
population values (called parameters) and the measured sample values (called statistics).
Sampling error arises any time you use a sample, even if your sample is random and unbiased. For this
reason, there is always some uncertainty in inferential statistics. However, using probability sampling
methods reduces this uncertainty.
Sampling error is the difference between a parameter and a corresponding statistic. Since in most cases
you don’t know the real population parameter, you can use inferential statistics to estimate these
parameters in a way that takes sampling error into account.
There are two important types of estimates you can make about the population: point estimates and
interval estimates.
A point estimate is a single value estimate of a parameter. For instance, a sample mean is a point
estimate of a population mean.
An interval estimate gives you a range of values where the parameter is expected to lie. A confidence
interval is the most common type of interval estimate.
While a point estimate gives you a precise value for the parameter you are interested in, a confidence
interval tells you the uncertainty of the point estimate. They are best used in combination with each
other.
Each confidence interval is associated with a confidence level. A confidence level tells you the
probability (in percentage) of the interval containing the parameter estimate if you repeat the study
again.

Descriptive and Inferential Statistics.docx

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