Frequency table

Frequency of data occurs when we classify statistical data in respect of either a variable or an attribute. What is a frequency table may be defined as a tabular representation of statistical data, usually in an ascending order, relating to a measurable characteristic according to individual value or a group of values of the characteristic under study.

In case, the characteristic under study is an attribute, say nationality, and then the tabulation is made by allotting numerical figures to the different classes the attribute may belong like, in this Example of a Frequency Table or Frequency Table Example, counting the number of Americans, Indians, British, French, German and so on.  The qualitative characteristic is divided into a number of categories or classes in the frequency table which are mutually exclusive and exhaustive and the figures against all these classes are recorded. The figure corresponding to a particular class, signifying the number of times or how frequently a particular class occurs is known as the frequency of that class. Thus, the number of Americans, as found from the given data, signifies the frequency of Americans. So we define frequency table is a statistical table that distributes the total frequency to a number of classes.

A frequency table is useful in other statistical applications such as finding the frequency polygon, plotting a histogram, bar charts and pie charts. The frequency tables are used both for qualitative and quantitative data.

To manage and operate on a date that is put into a frequency table is much easier than operating on raw or unclassified data. The table can be used to calculate mean, median and mode. Which in turn are useful in coming to many business or scientific decisions.  Frequency tables also find application in the field of code cracking, science, marketing surveys, census surveys etc.

Testing of hypothesis is dependent on the similarities and differences between the frequency tables involved.  Frequency table is also useful in finding the standard deviations and other measures of central tendencies. A frequency table is said to be skewed when the mean and median are different. The study of this skewedness forms the basis of many important decisions in business and stock market.

If we have the test scores of 35 students from total score of 10, then we can make a frequency table of the data. The first column would be the score from 0,1, to 10 and the second column would be the number of students in each score. That would make it a simple frequency distribution.

Significant figures rules and properties

What are significant figures?
Significant figures are important and interesting figures. Significant figure is the first non – zero digit of the number.
Rules of Significant figures
Following are the significant digits rules: -
1. Leading zeros in a number are not the significant figures. For example 0.008 has only one significant figure and that is 8.
2. Zeroes which are imbedded in between are always significant figures. For example, 24.07 have four significant figures.
3. If the decimal point is specified then only the trailing zeros are significant figures. For example, 400.00 have five significant figures and 400 has only one significant figure and that is 4.

Learn more about Definite Integral Examples also for better understanding.
Properties of Significant figures
1. Adding and Subtracting Significant figures:
Adding Significant figures - When the two numbers are added, the number of decimal places of the sum is always equal to the least number of decimal places in any of the numbers added.

Subtracting Significant figures - When the two numbers are subtracted, the number of decimal places of the difference is always equal to the least number of decimal places in any of the numbers subtracted.

2. Multiplication and Division of Significant figures:
Multiplying significant figures - When the two numbers are multiplied, the number of decimal places of the product is always equal to the least number of decimal places in any of the numbers multiplied.
Dividing significant figures - When the two numbers are divided, the number of decimal places of the product is always equal to the least number of decimal places in any of the numbers divided.

3. Rounding Significant figures: We should round off the figures if we have too many significant digits. We can round off any number using either of two ways: -
• If digit is smaller than 5 then the digit remains unchanged, such as 2.43 can be rounded off to 2.4
• If the digit is greater than 5 or then we should drop that digit and add one to the preceding digit, such as 2.47 can be rounded off to 2.5

Number Lines

In Math, number line is a line of any length which is used to place the real numbers in order. Real numbers include the positive numbers, negative numbers, zero, decimal numbers and even fractions.

What is a number line? As the name suggests, a number line is a line with numbers, numbers here mean, real numbers which consist of positive, negative, decimals, fractions including zero. Zero is called the origin. The line can be of any length according to the numbers we need to place on it.
There are many points on the number line, each of the point relates to a real number and again each number has a unique point that corresponds to it.
For example, 2.5 (2 ½) corresponds to a point on a number line that is halfway between 2 and 3.

Rules to remember:
On the number line,
1. the point zero is the origin
2. all the points to the right of the origin are positive numbers and
3. all the points to the left of the origin are negative numbers
4. The number is smaller if it is left of another
5. The number is greater if it is right of another
6. The distance between two numbers is the difference between the greater and the smaller number.
A number line is used for learning as to how to compare the negative and positive numbers
As we start moving from left to right on a number line, the number gets bigger and as we move from right to left, the number gets smaller

Number line template:

Integer Number line: On the number line, the point zero is the origin, all the points right to the origin are positive integers and all the points left to the origin are negative integers.

Decimal number line: 
We can place decimals on a number line. For which, each segment of the number line is divided into ten equal parts.

Let us place the point 3.5 on the number line.

  For a better understanding, let us place the following points on a number line,
A=1.8, B=2.6, C=4.2, D= -1.4