Rounding Data
When data is gathered and calculated, the final information presented tends to be rounded. On some occasions it may be necessary to round data, especially when rounding non-integer vales to integer values for simplicity and statistical representation. An example of this would be at the end of the calculations in sample weighting, the fractions you get are rounded to integers, since the data is based on physical objects which cannot have fractions, and so is considered extra for rounding purposes. Data may also me rounded in order for it to be understandable if the information is to be presented to other people, or just to keep important digits only to get an idea of scale. Extreme examples of this would be comparing the size of …show more content…
When considering significant figures, only the first digit above zero is considered, and then followed by any number of digits following. For example when representing numbers on a table and the number of digits is consistent in each answer (5 digits require the number 568 to become 00568), calculating the numbers would mean ignoring any digit before the first digit above 0, and to the left of a decimal point. When decimals are calculated, all 0s are considered after the decimal point, as they have significance to the value of the number and so cannot be ignored. An example of rounding to significant figures would be if 5.687545 were rounded to 3 significant figures, it would become 5.69. The reason the 8 becomes 9 is because the following digit, 7, was rounded up, and increases the value of the previous digit by 1. This applies to all digits being rounded; if the digit being rounded is 5 or above, then it is rounded up, and if it is below 5, it is rounded down, maintaining the previous digit’s value, and replaced by a 0 if there is no decimal before …show more content…
For example, when wanting the approximate value of something with 2.5 in the calculation, the number may be rounded to either 2 or 3 since these integers are the closest to the original value of the number. Reasons why estimates are used may be for approximate data for a sense of scale, such as when observing the measurements of a large scale structure like mountain having the number in the thousands may be enough information to know how big the structure is visually, without the necessity for complex numbers. An example of this would be the speed of light. In general representation, the speed of light is knows as around 300,000,000 metres/second, but when doing calculations, the number becomes more complex and is then considered 29,792,458 metres/second, which even then is rounded for information efficiency.
Systematic Errors
Systematic errors occur in experimental observations, and usually come from the measuring instruments used. The reasons why systematic errors can occur might be because there is something wrong with the instrument used to gather the data, or its data handling system may have issues. Another reason may be because the instrument used for gathering the data is wrongly used by the person collecting data. There are two types of systematic error when using instruments that have a linear response:
- Offset/ zero setting error:
When data is gathered and calculated, the final information presented tends to be rounded. On some occasions it may be necessary to round data, especially when rounding non-integer vales to integer values for simplicity and statistical representation. An example of this would be at the end of the calculations in sample weighting, the fractions you get are rounded to integers, since the data is based on physical objects which cannot have fractions, and so is considered extra for rounding purposes. Data may also me rounded in order for it to be understandable if the information is to be presented to other people, or just to keep important digits only to get an idea of scale. Extreme examples of this would be comparing the size of …show more content…
When considering significant figures, only the first digit above zero is considered, and then followed by any number of digits following. For example when representing numbers on a table and the number of digits is consistent in each answer (5 digits require the number 568 to become 00568), calculating the numbers would mean ignoring any digit before the first digit above 0, and to the left of a decimal point. When decimals are calculated, all 0s are considered after the decimal point, as they have significance to the value of the number and so cannot be ignored. An example of rounding to significant figures would be if 5.687545 were rounded to 3 significant figures, it would become 5.69. The reason the 8 becomes 9 is because the following digit, 7, was rounded up, and increases the value of the previous digit by 1. This applies to all digits being rounded; if the digit being rounded is 5 or above, then it is rounded up, and if it is below 5, it is rounded down, maintaining the previous digit’s value, and replaced by a 0 if there is no decimal before …show more content…
For example, when wanting the approximate value of something with 2.5 in the calculation, the number may be rounded to either 2 or 3 since these integers are the closest to the original value of the number. Reasons why estimates are used may be for approximate data for a sense of scale, such as when observing the measurements of a large scale structure like mountain having the number in the thousands may be enough information to know how big the structure is visually, without the necessity for complex numbers. An example of this would be the speed of light. In general representation, the speed of light is knows as around 300,000,000 metres/second, but when doing calculations, the number becomes more complex and is then considered 29,792,458 metres/second, which even then is rounded for information efficiency.
Systematic Errors
Systematic errors occur in experimental observations, and usually come from the measuring instruments used. The reasons why systematic errors can occur might be because there is something wrong with the instrument used to gather the data, or its data handling system may have issues. Another reason may be because the instrument used for gathering the data is wrongly used by the person collecting data. There are two types of systematic error when using instruments that have a linear response:
- Offset/ zero setting error: