Maharashtra Board Class 7 Maths part 2 Chapter 15 Statistics PDF Download

Statistics

Let's Learn. Average

The following table shows how many minutes Asmita took to cycle to school every morning, from Monday to Saturday.

We see from the table that she takes 18 minute on some days, 20 on others and even 22 minutes on one day. If we consider these six school days, what would you say is the approximate time she takes to cycle to school?

In mathematics, to make such an estimate, we find the 'average'. If we add together the number of minutes required on each day and divide the sum by six, the number we get is, approximately, the time required every day. It is the 'average' of all six numbers.

Average = Sum of the number of minutes taken to cycle to school on each of six days / Total days

\[= \frac{20 + 20 + 22 + 18 + 18 + 20}{6} = \frac{118}{6} = 19\frac{2}{3}\]

On an average, Asmita takes \(19\frac{2}{3}\) minutes to cycle to school every day.

Example

A school conducted a survey to find out how far their students live from the school. Given below is the distance of the houses of six of the students from the school. Let us find their average distance from the school.

950 m, 800 m, 700 m, 1.5 km, 1 km, 750 m

Solution:

To find the average, we must first express all the distances in the same units.

Average = Sum of the distance between home and school for six students / Total number of students

\[= \frac{950 + 800 + 700 + 1500 + 1000 + 750}{6} = \frac{5700}{6} = 950 \text{ m}\]

The average distance at which the students live from the school is 950 m.

Teacher's Note

Average helps us find one middle number from many numbers. In your house, if you spend 30 minutes on homework on Monday, 20 minutes on Tuesday, and 25 minutes on Wednesday, the average time is 25 minutes.

Exam Trick

Remember: To find average, add all numbers and divide by how many numbers there are. If your marks are 80, 90, 70, the average is (80+90+70)/3 = 80.

Points to Remember

Average means finding one number from many numbers.
We add all the numbers together and divide by how many numbers we have.
Average can be a decimal or fraction, even if all the numbers are whole numbers.
Average helps us understand data easily.
First make all measurements the same unit before finding average.

Let's Discuss.

Example

Rutuja practiced skipping with a rope all seven days of a week. The number of times she jumped the rope in one minute every day is given below.

60, 62, 61, 60, 59, 63, 58

Average = Sum of the number of jumps on seven days / Total number of days

\[= \frac{60 + 62 + 61 + 60 + 59 + 63 + 58}{7} = \frac{423}{7} = 60.42\]

Average number of jumps per minute = 60.42

The samples that we have of the quantity we are measuring are called 'readings' or 'scores'.

We know that the number of jumps will be counted in natural numbers. Never will there be a fractional number of jumps. However, their average can be a fractional number.

Now I Know!

Average = Sum of all scores in the given data / Total number of scores

Activity:

Make groups of 10 children, in your class. Find the average height of the children in each group.

With the help of your class teacher, note the daily attendance for a week and find the average attendance.

Teacher's Note

Average is used in schools every day. Your school calculates the average marks of all students in each class.

Exam Trick

Always add all numbers first, then divide by how many numbers you have. This simple step helps you find the correct average.

Points to Remember

Add all the numbers together.
Count how many numbers you added.
Divide the sum by the count.
The answer is the average.

Let's Learn. Frequency Distribution Table

Sometimes, in collected data, some scores appear again and again. The number of times a particular score occurs in a data is called the frequency of that score. In such cases a frequency table is made with three columns, one each for the score, the tally marks and the frequency.

1. In the first column, scores are entered in ascending order. For example, enter 1, 2, 3, 4, 5, 6 in order one below the other.

2. Read the scores in the data in serial order and enter a tally mark '|' for each in the second column of the table in front of that score, e.g. if you read the score '3', make a tally mark in front of 3 in the second column. Place four tally marks like this ||||, but make the fifth one like this ⊢⊣||. It makes it easier to count the total number of tally marks.

3. Count the total number of tally marks in front of each score and enter the number in the next, i.e. third, column. This number is the frequency of the score.

4. Lastly, add all the frequencies. Their sum is denoted by the letter N. This sum is equal to the total number of scores.

Making A Frequency Table Of The Given Information/ Data

Example

The distance at which some children live from their school is given below in kilometres.

1, 3, 2, 4, 5, 4, 1, 3, 4, 5, 6, 4, 6, 4, 6

Let us see how to make a frequency table of this data.

We strike off a score to indicate that it has been counted. The list of scores below shows that the first three scores have already been counted.

(N, 3, 2, 4, 5, 4, 1, 3, 4, 5, 6, 4, 6, 4, 6)

Teacher's Note

A frequency table helps us count things quickly when there are many items. In your school, teachers use frequency tables to count how many students got each mark.

Exam Trick

Use tally marks to count quickly. Make groups of 5 by drawing one line through 4 lines. This makes counting easier and reduces mistakes.

Points to Remember

Frequency means how many times something happens.
Tally marks help us count quickly.
Put scores in order from smallest to largest.
The total of all frequencies equals the total number of items.
A frequency table makes it easy to find average of large data.

This is a preview of the first 3 pages. To get the complete book, click below.