Consider an example that you have two weighing scales, the first one can weight in grams and second one is able to weight in milligrams as well. So to measure the accuracy of both the scales you weigh some packets of cheese slices. After placing cheese slices on scale 1 you get a reading of 756 grams while the second scale provides you with the measurement of 756.53 grams.
In the milligrams scale it would be 756530 milligrams, can you see what’s the difference in both the scales measurements although the object is same? Well, the first scale able to weight only in grams does not provide much accuracy and gives reading in 3 digits. These digits are known as the significant figures.
And for the second scale measurements, in the value 756530 milligrams there are 5 significant figures and in 756.53 grams the number of significant figures is the same. The significant digits are the numbers that have a contribution in a measurement or value.
Let us learn more useful information about significant figures and expected value in the article below.
Significant Figures
The number of a measurement or digits in a value that provide the accuracy in the value are known as the significant figures. The number that is provided in the form of digits is established using significant figures. These digits represent numbers in a meaningful way. Instead of figures, the phrase significant digits is also frequently used.
The first non-zero digit is where we begin counting significant figures. Thus by counting all the values starting with the first non-zero digit on the left, we may determine the number of significant digits. The number 23.12, for example, includes four significant digits.
Rules for Significant figures
- The significant figures are all of the non-zero digits in the value.
- Trapped zeros are the significant figures that occur between two non-zero digits.
- Leading zeros (zeroes preceding non-zero numbers) are not considered as significant.
- In any value without a decimal, the trailing zeros (zeroes after non-zero numbers) are usually not significant figure.
- The trailing zeros in any number with a decimal point are regarded as significant figures.
- In scientific notation, every number is called significant figure.
Rounding Significant Figures
The method of rounding to a significant figure is frequently employed since it may be applied to any number, no matter how large or small. When a newspaper publishes that 3 million people have condemned the government act, it is rounded to the nearest significant sum. It takes the most significant figure in the number and rounds it up. But instead of using same old method, we may also try the significant figures calculator
Expected Value
Among all the concepts of probability theory, the expected value concept for a random variable is the fundamental one. As the expected value in probability theory has a theoretical meaning. The expected value is what you would imagine an experiment’s average result to be.
The expected value tells you what to expect in a long-term experiment after several experiments. To define the expected value informally, we would say, a weighted average of all the possible values for X, with each value weighted according to the probability of that result to occur is known as the expected value of X in which the X is a discrete random variable. E(X) or m are common abbreviations for the expected value of X.
However, we write it as,
E(X) = S x P (X = x)
According to the equation we can say that by taking the sum of the product of every possible outcome and the probability of the outcome occurring the expected value can be calculated. We can do it manually as well as online by using online expected profit calculator.
Since the expected value is a central term of probability. In some ways, much more general than probability itself. The center of the variable’s distribution has represented by the expected value of a real-valued random variable.
We can calculate interesting features of distribution by taking the expected value of various functions of a general random variable. Such as spread, skewness, kurtosis, and correlation.
The distribution of a variable is entirely determined by generating functions, which are specific forms of expected values. Another basic principle of probability is conditional expected value, which integrates existing knowledge into the computation.
