Muhammad Imdad Ullah - Statistics for Data Analyst

Absolute Error of Measurement

Apr 29, 2024Apr 18, 2021 by Muhammad Imdad Ullah

The absolute error of measurement is the difference between the measured value of an object and its true value.

When we measure an object, the measured value may be either a little more or a little lower than its true value, that is, an absolute error has occurred.
For example, if a scale (a measurement device) states the weight 10KG but you know the true weight is about 9KG, then the scale has an absolute error of 1KG ($ 10KG-9KG=1KG$).

This error may be caused by the scale used itself ‌ not measuring the exact amount of measurement you are trying to measure. For example, your measuring device may be accurate to the nearest KG. That is, if the weight is 9.6 kg, your scale may “round up” and give 10 kg. Thus, the absolute error is about $ 10KG-9.6KG=0.4KG$.

Absolute Error of Measurement

Mathematically, it can be described by the formula given below,
$ (\Delta X)=X_i-X$, where $ X_i$ is the measurement quantity by the device used and $X$ is the true value.

The measurement device may either little more or a little lower than the true value, the formula can be described in absolute form, that is
$$(\Delta X)=|X_i-X| $$

‌Note that

If someones know the true value and the measured value, then the absolute error of measurement is just the subtraction of these numbers. However, sometimes, one may not know about the true value, one should use the maximum possible error as the absolute error.
Any possible measurement that one makes is ‌ an approximation, 100% accuracy of any measurement is impossible. It is also possible that if a measurement of the same object is made twice, then the two measurements may not be identical. Such ‌ differences between measurements (of the same object) are called variations in the measurement.
The absolute error of measurement does not provide any details about the graveness or importance of the error. For example, when measuring the distances between cities Kilometers apart, an error of a few centimeters is negligible. However, an error of centimeters when measuring a small piece of a machine is a ‌ significant error.
The largest possible absolute error of a measurement is always half of the value of the smallest unit used.

SPSS Data Analysis

Online MCQs Quiz Website

Basics of Ratios: Use and Application (2021)

May 4, 2024Apr 12, 2021 by Muhammad Imdad Ullah

This post will discuss some Basics of Ratios. The ratio is used to compare two quantities of the same kind. Consider in a group of 45 people, 15 of whom are females. Let us understand the Basics of Ratios from an example.

Example of Ratios

We can compare the number of males and the number of females in the group in two different ways,

There are 15 more males than females in a group of people. We are comparing the number of males and the number of females in the group of people by finding their differences.
The number of males in a group of people is twice that of females. We are comparing the number of males and the number of females by finding a fraction consisting of the number of males over the number of females. The fraction is $\frac{30}{15}$.

In the second method, the fraction obtained is an example of the ratio.

A ratio may be written with a colon symbol between the numbers. Therefore, the male-female ratio in the group of people can be written as 30:15 or $\frac{30}{15}$. It can be read as the ratio of 30 is to 15, or simply 30 to 15.

In general, the ratio of $a$ to $b$ can be written as $la:b$ or $\frac{a}{b}$, where $a$ and $b$ represent whole numbers and $b$ should not be zero. Since ratio $\frac{30}{15}=\frac{2}{1}$ or $30:15 = 2:1$. the $30:15$ and $2:1$ are called equivalent ratios.

Note that the order in which the ratio is written is important. A ratio has no measurement units. It is only a number that indicates how many times, one quantity is as great as the other. For example, the male to the female ratio of 2:1 means that the number of males is twice the number of females. It can also be interpreted as the female to male of 1:2 or $\frac{1}{2}$ indicates that there are half as many females as males.

Application of Ratios

Ratios can also be used to compare more than two quantities. For example, three-men A, B, and C share the profit of a business. They receive say 5000, 3000, and 1000, respectively. The ratio of their share of the profit is 5000:3000:1000 or 5:3:1.

One can also find that either there is an increase or decrease in the ratio. For example, say if the number of teachers in a college is increased from 45 to 55, then the ratio “number of present staff” to “number of old staff” (or number of present staff: number of old staff) = $55:45 = 11:9$ or $\frac{\text{no. of present staff}}{\text{no. of old staff}} = \frac{55}{45}=\frac{11}{9}$.
This ratio can be interpreted as the number of teachers has been increased in the ratio 11:9 or $\frac{11}{9}$.

The application of ratios in various fields are:

Finance (Financial rations, investment analysis)
Business and Management (inventory management, marketing and sales, and human resources)
Science and Engineering (Concentration and Ratios in Chemistry, Mixture Ratios, Scale and Proportion
Everyday Applications (Recipes, Maps and Scales)
Mathematics (Rates and Unit Costs, Proportions)

Remember, ratios are a versatile tool, and their specific applications can vary depending on the field and situation. However, their core principle of comparing quantities remains constant, making them a valuable asset for anyone seeking to analyze and understand the world around them.

SPSS Data Analysis

Online MCQs Quiz Website

Significant Figures: Introduction and Example (2021)

May 17, 2024Apr 5, 2021 by Muhammad Imdad Ullah

Rounding of numbers is done so that one can concentrate on the most significant digits. For example, consider a flat price at 285500. A rich man might think in hundreds of thousands of dollars. To a rich man, it is easier to think in terms of 1 significant figure, the “3” in 300,000. A wage might be worried about the hundreds of dollars. To him, there may be four significant figures, the ‘2’, ‘8’, ‘5’, and ‘5’ in 285500.

Significant Figures Example

Consider an example: A weight recorded as 8426kg is correct to 3 decimal places. Reporting this weight in grams, the 8425g is nearest to the whole number. Recording the weight as 8.426kg correct to 4 significant figures and converting the weight to 8426g, the number of significant figures is still 4. Thus, sometimes it is more useful to express a result in terms of numbers of significant figures rather than the number of decimal places.

There are some rules for writing significant figures:

Rule 1: Include one extra figure for consideration. Simply drop the extra figure if it is less than 5. If it is 5 or more, add 1 to the previous figure before dropping the extra figure.

Rule 2: All non-zero digits are significant wherever they are recorded. For example, 7.22 is correct to 3 significant figures.

Rule 3: Zeros that lie between non-zero digits are significant. For example, 2003 is correct for 4 significant figures.
Rule 4: Zeros that are not preceded by a non-zero digit (leading zeros) are not significant. For example, 0.000325 is correct to 3 significant digits.

Rule 5: Zeros that appear after the decimal points (trailing zeros) but are not followed by a non-zero digit are significant. For example, there are 5 significant digits in 22.300.

Rule 6: The final zeros in a whole number may or may not be significant. It depends on how the estimation is made.

A point to remember is that the number of digits is used to denote an exact value to a specified degree of accuracy. For example, 6084.324 is a value accurate to 7 significant figures. If written as 6080 it is accurate to 3 significant digits. The final 0 is not significant because it is used to show the order of magnitude of the number.

List of Inferential Statistics and Description

Learn R Programming Language

Percentages, Fractions, and Decimals Made Easy

May 4, 2024Apr 1, 2021 by Muhammad Imdad Ullah

Percentages, Fractions, and Decimals are connected. Percentages, fractions, and decimals are all different ways to represent parts of a whole. They can be converted between each other, which is useful for solving many mathematical problems.

We often see phrases like

up to 75% off on all items
90% housing loan with low-interest rates
10% to 50% discount advertisements

Examples of Percentages, Fractions, and Decimals

These are some examples of percentages.

Suppose, there are 200 students in a college. Let 80 students remain in college to participate in college extra-curricular activities (ECA). The fraction of students who participated in college ECA can be written as $\frac{80}{100}$, or $\frac{40}{100}$, or $\frac{2}{5}$. We can read it as 80 out of 200 students participated in ECA (or 2 out of 5 participated in ECA). Multiplying this fraction with 100 will convert the fraction to percentages. Therefore, 40% of the students participated in ECA.

By percent means that for every hundred or out of every hundred.

Therefore, a percentage is a fraction whose denominator is always 100. Therefore, a percentage can be converted to a fraction by dividing it by 100. Alternatively, one can change a fraction or a decimal to a percentage by multiplying it by 100. The following figure is about the conversion cycle of percentages to fractions or decimals and vice versa.