Meaning of Statistics

Statistics is the part of mathematics that deals with collecting information (data), arranging it in order, showing it clearly, studying it, and then making useful decisions.

Data means information or facts collected about people, objects, or events.

Statistics helps us to summarize large numbers so that they are easy to understand.

Example:

If we want to know the most common shoe size in a class of 50 students, it is difficult to look at every student’s shoe size one by one. But if we use statistics, we can arrange the sizes in a table or chart, and easily see the most common size.

Purpose of statistics

1. Statistics helps us to study and understand information clearly.


2. It helps us to compare different groups of data.


3. It helps us to make wise decisions in daily life, school, business, and government.

Why we need to collect data

1. To have correct and reliable information.


2. To avoid guesswork or wrong decisions.


3. To plan properly for the future.

Example:
Before building classrooms, a school must collect data on the number of students who need seats. If the data is not collected, the school may build too few or too many classrooms.

1. Collection of data: Gathering information or facts.
   Example: Asking all students in a class their ages.


2. Organization of data: Arranging the collected information in a clear form such as a table.


3. Presentation of data: Showing the data using bar charts, pie charts, histograms, tables, or line graphs.
   Example: Showing favourite fruits of students in a pie chart.


4. Analysis of data: Studying the data to see patterns, trends, or answers.


5. Interpretation of data: Drawing conclusions or making decisions from the results.
   Example: If 20 out of 30 students like mango, we can conclude that mango is the most popular fruit in the class.

Data can be collected in different ways:

1. Interview: Asking people questions directly.


2. Questionnaire: Giving people written questions to answer.


3. Observation: Watching events and recording information.


4. Records: Checking books, documents, or registers.

Classroom activity example: Collect the number of brothers and sisters each student in your class has.

After collecting data, we can present it in many ways:

1. Frequency table with tally marks: A table that shows how many times each value occurs.


2. Bar chart: Rectangles of equal width used to compare data.


3. Histogram: Bars that touch each other, used to show continuous data.


4. Pie chart: A circle divided into parts to represent data.


5. Line graph: A graph made by joining points with straight lines.

These are ways of finding the central value of data.

Mean (average)

Formula:
Mean = (Sum of data) ÷ (Number of data)

Example: Ages = 10, 12, 14 → Mean = (10+12+14) ÷ 3 = 36 ÷ 3 = 12.

Median

The middle value when data is arranged in order.

1. For odd numbers of data: Median is the middle number.
   Example: 5, 7, 9 → Median = 7.


2. For even numbers of data: Median is the average of the two middle numbers.
   Example: 6, 8, 10, 12 → Median = (8+10) ÷ 2 = 9.

Mode

The value that occurs most often.

Example: 2, 3, 3, 4, 5 → Mode = 3.

Statistics is very important in our daily life because:

1. It helps us to know and understand large amounts of information easily.


2. It helps us to compare different groups or situations (for example, comparing exam results of two classes).


3. It helps us to make correct decisions in schools, businesses, hospitals, and government.


4. It helps us to plan properly for the future, like how many teachers or classrooms are needed.


5. It helps us to find patterns and solve problems, such as knowing the most common sickness in a community or the most common product customers buy.

Question 1 – Frequency Table

The marks scored by 10 students in a test are:

5, 7, 8, 5, 6, 8, 7, 5, 6, 8.

Prepare a frequency table.

Solution (Steps):

List out the distinct values: 5, 6, 7, 8.

Count how many times each occurs.

5 appears 3 times.

6 appears 2 times.

7 appears 2 times.

8 appears 3 times.

Answer (Frequency Table):

Marks	Frequency
5	3
6	2
7	2
8	3

Question 2 – Mean

Find the mean of these numbers:

12, 14, 16, 18.

Solution (Steps):

Add the numbers: 12 + 14 + 16 + 18 = 60.

Count the numbers: 4.

Divide: Mean = 60 ÷ 4 = 15.

Answer:

The mean = 15.

Question 3 – Mean from Frequency Table

The shoe sizes of students are given:

Shoe Size	38	39	40
Frequency	2	3	5

Find the mean shoe size.

Solution (Steps):

Multiply each size by its frequency:

38 × 2 = 76

39 × 3 = 117

40 × 5 = 200

Add them up: 76 + 117 + 200 = 393.

Total frequency = 2 + 3 + 5 = 10.

Mean = 393 ÷ 10 = 39.3.

Answer:

The mean shoe size = 39.3.

Question 4 – Median (Odd Numbers)

Find the median of:

6, 8, 3, 5, 9.

Solution (Steps):

Arrange in order: 3, 5, 6, 8, 9.

Since there are 5 numbers (odd), pick the middle one.

Middle = 6.

Answer:

Median = 6.

Question 5 – Median (Even Numbers)

Find the median of:

4, 8, 6, 10.

Solution (Steps):

Arrange in order: 4, 6, 8, 10.

There are 4 numbers (even), so take the average of the middle two.

Middle two = 6 and 8 → (6 + 8) ÷ 2 = 14 ÷ 2 = 7.

Answer:

Median = 7.

Question 6 – Mode

The ages of children are:

7, 9, 8, 7, 6, 9, 7, 10, 9.

Solution (Steps):

Count frequency of each:

6 → 1 time

7 → 3 times

8 → 1 time

9 → 3 times

10 → 1 time

Highest frequency = 3.

Both 7 and 9 appear 3 times.

Answer:

Mode = 7 and 9 (bimodal).

Question 7 – Real-Life Example

The favourite fruits of students in a class are:

Mango, Mango, Orange, Mango, Orange, Banana, Orange, Orange.

Find the most popular fruit.

Solution (Steps):

Count each fruit:

Mango = 3

Orange = 4

Banana = 1

The one with the highest frequency = Orange.

Answer:

The most popular fruit is Orange.

Question 8 – Total Frequency

The table shows ages of pupils:

Age	10	11	12	13
Freq	2	5	6	7

Find the total number of pupils.

Solution:

Add frequencies: 2+5+6+7 = 20.

Answer:

Total pupils = 20.

Question 9 – Mean Marks

Marks of 5 students: 20, 25, 30, 15, 10.

Solution:

Sum = 20+25+30+15+10 = 100.

Count = 5.

Mean = 100 ÷ 5 = 20.

Answer:

Mean = 20.

Question 10 – Range

The ages are: 12, 15, 10, 18, 20.

Solution:

Largest = 20, smallest = 10.

Range = 20 – 10 = 10.

Answer:

Range = 10.

Question 11 – Mode of Shoe Sizes

Shoe sizes: 39, 40, 38, 40, 41, 39, 40.

Solution:

Frequencies:

38 → 1, 39 → 2, 40 → 3, 41 → 1.

Highest = 40.

Answer:

Mode = 40.

Question 12 – Median of Even Data

Find the median of: 12, 15, 20, 25, 30, 35.

Solution:

Ordered: already arranged.

Middle = (20+25) ÷ 2 = 22.5.

Answer:

Median = 22.5.

Question 13 – Favourite Colour Survey

In a class of 12:

Red = 5, Blue = 4, Green = 3.

Which colour is most popular?

Solution:

Highest frequency = 5 (Red).

Answer:

Most popular colour = Red.

Question 14 – Bar Chart Reading

A bar chart shows pupils’ pets:

Dogs = 8, Cats = 5, Birds = 3.

How many pets in total?

Solution:

Add: 8 + 5 + 3 = 16.

Answer:

Total pets = 16.

Question 15 – Mean from Survey

Number of siblings in a class:

Siblings	0	1	2	3
Freq	2	3	4	1

Find mean number of siblings.

Solution:

Multiply:

0×2 = 0, 1×3 = 3, 2×4 = 8, 3×1 = 3.

Sum = 0 + 3 + 8 + 3 = 14.

Total frequency = 2 + 3 + 4 + 1 = 10.

Mean = 14 ÷ 10 = 1.4.

Answer:

Mean = 1.4 siblings.

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Conclusion

Statistics is very useful because it helps us to collect, organize, present, and understand information easily.

It helps us to make good decisions in our schools, homes, businesses, and government.

By learning statistics, we can solve real-life problems using data in a clear and simple way.