Count of valid cells. The prefixed

COUNTA

COUNT

function is very useful in counting.

STDEV STDEVA Standard deviation

Standard deviation from a population or

STDEVP STDEVPA a very large sample (relative to

population)

VAR VARA Variance

Variance from population (and not

VARP VARPA sample) data, or from a very large

sample (relative to population)

MIN MINA Minimum value

MAX MAXA Maximum value

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Statistical Analysis with Excel

CHAPTER 7

PROBABILITY DENSITY FUNCTIONS AND

CONFIDENCE INTERVALS

This chapter teaches the following topics

” PROBABILITY DENSITY FUNCTION (PDF)

” CUMULATIVE DENSITY FUNCTION (CDF)

” THE CDF AND CONFIDENCE INTERVALS

” INVERSE MAPPING FUNCTIONS

” NORMAL DENSITY FUNCTION

” STANDARD NORMAL OR Z“DENSITY FUNCTION

” T“DENSITY FUNCTION

” F“DENSITY FUNCTION

” CHI-SQUARE DENSITY FUNCTION

” OTHER CONTINUOUS DENSITY FUNCTIONS: BETA, GAMMA,

EXPONENTIAL, POISSON, WEIBULL & FISHER

” DISCRETE PROBABILITIES” BINOMIAL, HYPERGEOMETRIC

& NEGATIVE BINOMIAL

” LIST OF DENSITY FUNCTION FUNCTIONS ” PROBABILITY

DENSITY FUNCTION (PDF), CUMULATIVE DENSITY

FUNCTION (CDF)

” LIST OF SELECT INVERSE FUNCTION

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Chapter 7: Probabiity Density Functions & Confidence Intervals

PROBABILITY DENSITY FUNCTIONS (PDF),

7.1

CUMULATIVE DENSITY FUNCTIONS (CDF), AND

INVERSE FUNCTIONS

7.1.A PROBABILITY DENSITY FUNCTION (PDF)

Figure 101: Probability Density Function (PDF)

The horizontal axis contains the values of the series/series. The vertical

height of the curve at a point on the X“axis shows the probability

associated (or frequency) with that point. (The total area under the curve

equals 1; so, all the “heights” add up to 1 or 100 %.) The higher the

frequency with which that point is observed in a series/series, the higher

is its frequency.

An often“used probability Density Function ” the “Normal” probability

Density Function ” is shown in the previous figure. This Density

Function has some convenient properties:

” its Mean, Mode and Median are the same

” it does not have a left or right skew, and

” the left half is a mirror image of the right half.

All these “symmetrical” properties allow one to draw inferences from tests

run on series that are distributed “Normally.”

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Statistical Analysis with Excel

Based on several theorems, postulate, “most data series start behaving

more and more like a series that follows a Normal Density Function as

the sample size (or number of data points) increases.” (This presumption

follows from the “Central Limit Theorem.”) This has made the Normal

Density Function the bedrock of most statistics and econometrics.

7.1.B CUMULATIVE DENSITY FUNCTION (CDF)

We are typically interested in measuring the area under the curve (a) to

the left of an X value (b) to the right of an X value, or (c) between two X

values. The height of the curve at any X value is not so useful by itself

because it does not answer any of these questions directly.