Data Analysis With Graphs

Data Analysis is the process of inspecting, organizing, and interpreting data to uncover useful patterns and insights. In simple terms, it involves examining numbers and facts to understand their meaning. This helps in identifying trends and making informed decisions. Graphs and statistical methods are often used to present information clearly.

Statistics

Statistics is the study of collecting, organizing, and understanding numbers (data). It helps us answer questions like “How many people like chocolate?” or “What is the average height of students?”

Types of Variables

Continuous Variables: Numbers that can be any value in a range (like height, weight, or temperature).
Discrete Variables: Whole numbers that don’t change smoothly (like the number of students in a class).

Ways to Show Data (Graphs)

Histogram: A bar graph that shows how often numbers appear in a range

Frequency Polygon: A line graph that connects points to show trends
Pie Chart: A circle divided into parts (like a pizza) to show percentages

Biased Source

If data is collected unfairly, it can give wrong information. For example, if you ask only basketball players about their favorite sport, most will say basketball. This is biased!

Classes and Intervals

When data has many numbers, we put those values into groups called classes or intervals. For instance, if we consider people's ages, we can group them as 0-10, 11-20, 21-30, etc.

Frequency & Relative-Frequency

Frequency refers to the amount of times something appears in data. For instance, if a student scores 80 on a test 3 times, the frequency of 80 is 3
Relative frequency refers to the fraction or percentage of times something appears. For instance, if 3 students score 80 out of 10 total students, the relative frequency is 3/10 or 30%

What is wrong with the intervals in this table?

Age (years)
28–32
33–38
38–42
42–48
48–52

Show Answer

The problem is that some intervals overlap. For example, the number 38 could be in both the 33–38 and 38–42 intervals. The intervals should not overlap. You could fix it like this:

Age (years)
28–32
33–37
38–42
43–47
48–52

For the number of apples, bananas, oranges, etc., sold in a store. Would you use a histogram or bar graph?

Show Answer

You would use a bar graph. This is because the data is about categories (types of fruit), and bar graphs are used for categorical data.