Q.By multiplying each of the numbers 3, 6, 2, 1, 7, and 5 by 2 and then adding 5, we obtain the set 11, 17, 9, 7, 19, 15. What is the relationship between the standard deviations and the means for the two sets?

Types of Data: From Intuition to Precision

Imagine you walk into a classroom and want to describe the students. You could say things like "five students wear glasses," "the average height is 160 cm," or "most students prefer cricket over football." Each of these statements uses a different kind of information. That difference is what "types of data" is about.

Data is just a collection of facts. But not all facts are the same. Some facts are categories (like "cricket" or "football"), some are numbers you can count (like "5 students"), and some are numbers you can measure (like "160 cm"). The type of data tells you what you can do with it — what calculations make sense, what graphs to draw, and what conclusions you can draw.

The Two Big Families

All data falls into one of two broad families:

Qualitative (Categorical) Data — data that describes qualities or categories. It answers "which kind?" or "what type?"

Quantitative (Numerical) Data — data that involves numbers. It answers "how many?" or "how much?"

Qualitative Data: Names and Labels

This is data that can be sorted into groups, but you cannot do arithmetic on it. For example:

• Eye colour (brown, blue, green)
• Favourite subject (Maths, Science, English)
• Gender (Male, Female, Other)
• City of residence (Delhi, Mumbai, Chennai)

You can count how many students are in each group, but you cannot add "brown" to "blue" or find the average of "Maths" and "Science."

Qualitative data splits further into two types:

Nominal Data — categories with no natural order. Eye colour is nominal: brown is not "greater than" blue. There is no ranking.

Ordinal Data — categories that do have a natural order, but the gaps between them are not equal. For example, survey responses: "Very satisfied," "Satisfied," "Neutral," "Dissatisfied," "Very dissatisfied." You know "Very satisfied" is better than "Satisfied," but you cannot say it is exactly twice as good.

Quantitative Data: Numbers You Can Work With

This is data that comes from counting or measuring. You can add, subtract, average, and do all sorts of maths with it.

Quantitative data also splits into two types:

Discrete Data — data that can only take specific, separate values. Usually these are whole numbers from counting. Examples: number of students in a class (you cannot have 30.5 students), number of cars in a parking lot, number of heads when flipping a coin 10 times.

Continuous Data — data that can take any value within a range. These come from measurement. Examples: height (could be 160.2 cm, 160.23 cm, etc.), temperature, time, weight.

The Complete Picture

Here is the full classification in one table: