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Statistics is the number based information. The numbers used for information are data of statistics.

Thus, we need a clear understanding of data and information to study statistics.

Data vs Information

Data are the raw elements. They are not meaningful on their own. For example: a list of numbers 33, 50, 80.

Information is the finished product. After processing, organizing and giving a context the raw data becomes meaningful information. For example: if we say the numbers mentioned above are marks obtained by 3 students out of 100, it becomes meaningful information.

Types of Data

Data can be of 3 different types. i) Discrete, ii) Continuous, iii) Categorical.

Discrete data can be listed. It often represent whole numbers, and there are gaps between them. It usually involves a count of something, such as number of students in a class.

Continuous data can take any value between a range. It often takes fractional values. It usually involves a measurement of something, such as height of a person.

Population vs Sample

Population is the entire group of individuals, objects, or items that a researcher wants to study and draw conclusions about.

Sample is a smaller, manageable subset of the population.

Let's understand population and sample with examples. Suppose a researcher wants to investigate a prediction: "Newborn baby boys are heavier than newborn baby girls." In this case, all newborn babies are population. But it is very difficult to find the masses of all the newborn babies. So, it is easier and manageable to find the masses of a group of newborn babies which is our sample in this case.

While choosing the sample, we need to be careful. If the sample is too small compared to the population, it may fail to represent the population accurately.

Mean

Mean is the sum of the numerical values of data divided by the number of data.

∴ Mean = \frac{Sum of numbers}{Number of numbers}

Problems:

1. These are marks obtained by students in an exam: 7, 8, 9, 10, 11. Find the mean.

Median

The value which divides the organized data into two equal parts is the median.

If there is 'n' number of data and 'n' is an odd number then median is the value of

(\frac{n + 1}{2})

^th term.

If there is 'n' number of data and 'n' is an even number then median is the average value of

(\frac{n}{2})

th term and

(\frac{n}{2} + 1)

^th term.

Median Problems

1. Find the median of the following numbers: 33, 21, 35, 25, 31, 22, 27, 28, 37, 39, 40, 26, 29.

2. Find the median of the following numbers: 23, 11, 25, 15, 21, 12,17, 18, 22, 27, 29, 30, 16, 19.

Mode

The number which appears maximum times is the mode of the data.

Mode Problems

1. Find the mode of the following numbers: 11, 9, 10, 12, 11, 12, 14, 11, 10, 20, 21, 11, 9, 18.