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Connecting the Dots – Class 7 Mathematics notes, important questions and MCQs

NCERT Class 7 Mathematics, chapter 13. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Data helps us answer questions about the world. We first decide whether a question is statistical, then collect data, find a representative value such as the mean or median, and show the data with tables and graphs. We must also read graphs carefully because they can mislead.

Questions and representative values

A statistical question expects answers that vary, such as 'How many hours do students of my class sleep?'; 'How old am I?' is not statistical.
The mean (average) = sum of all values ÷ number of values.
The median is the middle value when data is arranged in order; for an even number of values it is the average of the two middle values.
The median is less affected than the mean by a few very large or very small values.

Visualising data

Pictographs use pictures; each symbol stands for a fixed number of items.
Bar graphs use bars of equal width with heights proportional to the values; double bar graphs compare two sets of data.
A good graph has a title, labelled axes and a suitable, uniform scale.

Being a data detective

Graphs can mislead when the scale does not start from zero, the scale is uneven or pictures are drawn in different sizes.
Always check the source of data, the sample size and the scale before drawing conclusions.

Key terms

Mean: the sum of the values divided by the number of values
Median: the middle value of data arranged in order
Bar graph: a graph that shows data with bars of equal width and heights proportional to values
Scale: the number of units each division or symbol on a graph stands for

Formulas

Mean = (sum of values) ÷ (number of values)
Median (odd n) = value at position (n + 1) ÷ 2 after ordering

Important questions with answers

What is the difference between mean and median?2 marks

The mean is found by adding all the values and dividing by the number of values. The median is the middle value when the data is arranged in order. The mean is affected by very large or very small values, while the median is not much affected by them.

Find the mean and median of 7, 3, 9, 5, 11.3 marks

Sum = 7 + 3 + 9 + 5 + 11 = 35, and there are 5 values, so mean = 35 ÷ 5 = 7. Arranged in order: 3, 5, 7, 9, 11; the middle (3rd) value is 7, so the median is 7.

Explain three ways in which a graph can mislead readers, and how a careful reader can check a graph.5 marks

First, the vertical axis may not start at zero; then a small difference such as 92 and 95 can look like one bar is many times taller than the other. Second, the scale may have unequal steps, for example 0, 10, 20, 50, 100, which distorts the picture. Third, in pictographs the symbols may be drawn in different sizes, so a larger picture seems to show much more even when the numbers are close. A careful reader checks the title and labels, looks at where the scale starts and whether the steps are equal, reads the actual numbers, checks the source of the data and the sample size, and only then draws conclusions.

Quick revision

Statistical question = answers vary.
Mean = sum ÷ count; median = middle value.
Extreme values pull the mean, not the median.
Check scale, title and labels of every graph.

Exam tips

Always arrange data in order before finding the median.
Before trusting a graph, look at where the scale starts and whether steps are equal.

Practice MCQs

The mean of 4, 6 and 8 is
1. 5
2. 6
3. 7
4. 18
Show answer
Answer: (b) 6. (4 + 6 + 8) ÷ 3 = 6.
The median of 3, 9, 5 is
1. 3
2. 5
3. 9
4. 17
Show answer
Answer: (b) 5. In order 3, 5, 9 the middle value is 5.
Which of these is a statistical question
1. How tall are the students in my class
2. How tall am I
3. What is 5 + 3
4. What is my name
Show answer
Answer: (a) How tall are the students in my class. Its answers vary from student to student.
The median of 2, 4, 6, 8 is
1. 4
2. 5
3. 6
4. 20
Show answer
Answer: (b) 5. Average of the two middle values (4 + 6) ÷ 2 = 5.
In a pictograph one symbol stands for 10 books. Four and a half symbols show
1. 4.5 books
2. 40 books
3. 45 books
4. 50 books
Show answer
Answer: (c) 45 books. 4.5 × 10 = 45.
Marks of 5 students are 10, 12, 14, 16 and 98. Which value better represents the class
1. the mean
2. the largest mark
3. the median
4. the sum
Show answer
Answer: (c) the median. The median (14) is not pulled up by the extreme mark 98.
The mean of five numbers is 20. If one number is removed, the mean of the rest becomes 18. The removed number is
1. 18
2. 20
3. 28
4. 30
Show answer
Answer: (c) 28. Sum 100 − 4 × 18 = 100 − 72 = 28.
A bar graph's vertical scale starts at 90 instead of 0. This can
1. hide the title
2. make all bars equal
3. make small differences look very large
4. change the data values
Show answer
Answer: (c) make small differences look very large. Cutting the axis exaggerates differences.

All chapters of Class 7 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.