Learn about collecting, organizing, and interpreting data through these examples with detailed step-by-step explanations.
Example 1: Introduction to Data Collection
What is 'Data' in Statistics and how is it collected?
Step 1: Understand 'Data'. Data is a collection of facts, such as numbers, words, measurements, observations, or just descriptions of things. In statistics, data is usually numerical.
Step 2: Learn about data collection. Data can be collected in many ways, including surveys (asking questions), observations (watching and recording), experiments (testing), and accessing existing records.
Step 3: Recognize different types of data. Data can be primary (collected directly by the researcher) or secondary (collected by someone else). It can also be quantitative (numerical) or qualitative (descriptive).
Example 2: Organizing Data into a Frequency Table
The marks obtained by 15 students in a test are: 10, 12, 8, 10, 15, 12, 10, 8, 12, 10, 15, 8, 10, 12, 10. Organize this data using a frequency table.
Step 1: Identify the distinct data values. The marks obtained are 8, 10, 12, and 15.
Step 2: Create a table with three columns: 'Marks Obtained', 'Tally Marks', and 'Frequency'.
Step 3: Go through the data one by one and put a tally mark ( | ) in the 'Tally Marks' column against the corresponding mark. For every fifth tally mark, cross the previous four ( | | | | ) to make a group of five.
Step 4: Count the tally marks for each distinct mark and write the total in the 'Frequency' column. Frequency is the number of times a particular value appears in the data.
Step 5: The completed frequency table shows how many students got each mark.
Step 6:
Frequency Table:
Marks Obtained
Tally Marks
Frequency
8
| | |
3
10
| | | | | |
6
12
| | | |
4
15
| |
2
Total
15
Example 3: Calculating the Mean (Average)
Find the mean of the following set of numbers: 5, 10, 15, 20, 25.
Step 1: Understand the Mean. The mean, or average, is calculated by adding up all the numbers in a data set and then dividing by the count of those numbers.
Step 2: Sum the numbers in the data set. Sum = 5 + 10 + 15 + 20 + 25 = 75.
Step 3: Count how many numbers are in the data set. There are 5 numbers.
Step 4: Divide the sum by the count. Mean = Sum / Count.
Mean = 75 / 5 = 15.
Step 5: The mean of the numbers 5, 10, 15, 20, 25 is 15.
Example 4: Finding Mean from a Simple Frequency Table
Find the mean marks from the following simple frequency table:
Marks (x)
Frequency (f)
10
3
20
2
30
1
Step 1: To find the mean from a frequency table, we need the sum of all observations and the total frequency (total number of observations).
Step 2: Multiply each 'Marks' value (x) by its corresponding 'Frequency' (f) to get the product (fx).
10 x 3 = 30
20 x 2 = 40
30 x 1 = 30
Step 3: Sum all the products (fx). Sum of fx = 30 + 40 + 30 = 100.
Step 4: Sum the frequencies to find the total number of observations. Total frequency = 3 + 2 + 1 = 6.
Step 5: Calculate the mean using the formula: Mean = Sum of fx / Total Frequency.
Mean = 100 / 6.
Note: This basic solver can calculate the mean of a list of numbers. Enter numbers separated by commas or spaces (e.g., "find the mean of 10, 20, 30", "average of 5 7 9").
Related Concepts
Explore these related mathematical concepts to deepen your understanding of Statistics.
Data
A collection of facts, such as numbers, words, measurements, observations, or descriptions.
Raw Data
Data collected in its original form, before being organized.
Frequency
The number of times a particular observation occurs in a data set.
Frequency Distribution Table
A table that lists each distinct data value and its frequency.
Mean
The average of a set of numbers (Sum of data / Number of data points).
Observations
The individual values or entries in a data set.
Range
The difference between the highest and lowest values in a data set.
Median
The middle value in a data set when arranged in order.
Mode
The value that appears most frequently in a data set.