Engineering Data Statistics

Histogram​

Also called Frequency Histogram.​

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It consist of a set of rectangleshaving a.) bases equal to the classinterval sizes with centers at theclass marks and b.) heights equalto the corresponding classfrequencies. ​

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The areas of the rectangles,therefore, are proportional to theclass frequencies.​

FrequencyPolygon

A line graph of class frequencyplotted against the class mark. ​

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It can also be obtained byconnecting the midpoints of thetops of the rectangle in thehistogram.​

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Ogive

it is also called CumulativeFrequency Polygon.​

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A line graph showing thecumulative frequency plottedagainst any class boundary. ​

Stem and Leaf Display​

The following are suggested steps in constructing astem and leaf display.​

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1. Select one or more leading digits for the stemvalues. The remaining digits become the leaves.​

2. List all the possible stem values in a verticalcolumn.​

3. Record the leaf for every observation beside thecorresponding stem value.​

4. Indicate the units for stems and leaves someplacein the display.​

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A display having between 5 and 20 stems isrecommended.​

Frequency Curves and Smoothed Ogives​

In the population, so many observations are available so that it istheoretically possible (for continuous data) to choose class intervals verysmall. Thus, the frequency polygon for large population have so manysmall broken line segments that they approximate curves, which we callthe frequency curves.​

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By smoothing the frequency polygon of the sample, theoretical curves ofthe population can be approximated.​

Types of Frequency Curves​

1. Symmetrical or Bell-shaped​

2. Moderately asymmetrical or skewed

3. J-shaped or reverse J-shaped​

4. U-shaped​

5. Bimodal​

6. Multimodal​

Numerical Summary​ Measures​

It can be calculated from either a sample or a population. ​

Parameter​

Any quantitativemeasure that describesa characteristics of apopulation.​

Statistic​

When it describes acharacteristics of asample.​

Mean or Arithmetic Mean​

It is the overall average

Population Mean

If the data represents the entire population.

Sample Mean

If the data represent the sample drawn from the population.

Median​

The median of a set of numbers in an array is either the middlevalue or the arithmetic mean of the two middle values.​

Mode​

is the value which occurs with the greatest frequency in a dataset. Along with mean and median, ____is a statistical measures of central tendency in a dataset, ____ may be several in a dataset.

3 Measures of Variability

Range, Variance, and Standard Deviation

Range

Is the simplest measure of variability. It is the least satisfactory because it provides no information at all about the data between the highest and the lowest values. ​

Variance​

It is a measure that considers the position of each observation relative to the mean. It is defined as the square of all the deviation

Population Variance

It tells how data points in a specific population are spread out

Sample Variance

It is used to calculate how varied a sample is.

A Statistic that estimates the true parameter on the average is said to be unbiased .

Standard Deviation 

It is the positive square root of the variance.

Probability

The extent to which an event is likely to occur, measured by the ratio of favorable cases to the whole number of cases possible.

Statistics

Science that deal with methods of collecting, presenting, and analyzing of data so that valid conclusion can be drawn from them.

Two Major Areas of Statistics

Descriptive Statistics
Inductive Statistics

Descriptive Statistics

Drawing data without inferring conclusion.

Inductive Statistics

Using mathematical tools to make forecast or inferences

Data Presentation

Visual techniques, tables and graphs.

Numerical Summary

Measures for data set

Measures of Central Tendency

Average middle values of dataset

Describes the center position of a distribution for a data set.

Measures of Variability

Dispersion of Data

Measures of Frequency Distribution

Number of times a data point occurs and how many times it fails to occur

Population

All of the conceivable members of a group under study.

Sample

Sub collection of items drawn from a population to study

Variables

The characteristics that is being studied

Stratified Sampling

Entails population units into non overlapping groups and taking a sample from each one

Frequency Distribution

the organization of data in tabular form gives the frequency distribution.

Raw Data

Data that have not been organized numerically

Array

Arrangement of raw data in ascending or descending manner.F

Frequency 

The number of times a value appears on listing.

Relative Frequency

Actual frequency over the total frequency

Class Interval

Lower Limit and Upperlimit

Class Limit

Define upper and lower values of data group

Class Boundaries

represents halfway point between successive classes.

Class Mark

Midpoint of class Interval

Classes

Represents grouping or classification.