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How Quantities Combine: Understanding Data – Class 9 Mathematics notes, important questions and MCQs

NCERT Class 9 Mathematics, chapter 10. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Data is collected, organised in tables and graphs, and summarised by measures of central tendency — mean, median and mode.

Organising data

Raw data → frequency table → grouped frequency table (class intervals).
Graphs: bar graph, histogram (no gaps, for grouped data), frequency polygon.
Primary data is collected yourself; secondary data comes from other sources.

Central tendency

Mean = sum of observations / number of observations.
Median = middle value after arranging in order; for even n, average of the two middle values.
Mode = most frequent value.

Key terms

Frequency: number of times a value occurs
Class interval: a group range like 10–20
Histogram: bar graph of grouped data with touching bars

Formulas

Mean x̄ = Σx / n
Median (odd n) = ((n + 1)/2)th value
Range = highest − lowest

Important questions with answers

Find the mean of 5, 8, 12, 15, 10.2 marks

Sum = 50, number of values = 5, mean = 10.

Find the median and mode of 4, 7, 2, 7, 9, 3, 7, 5.3 marks

Arranged: 2, 3, 4, 5, 7, 7, 7, 9. n = 8, median = (5 + 7)/2 = 6. Mode = 7 (occurs 3 times).

The marks of 20 students are: 10 students scored 40, 6 scored 60 and 4 scored 80. Find the mean, median and mode, and say which measure best represents the class.5 marks

Mean = (400 + 360 + 320)/20 = 1080/20 = 54. Arranged in order, the 10th and 11th values are 40 and 60, so median = 50. Mode = 40 (most frequent). The mean (54) uses all scores and is a good overall summary here; the mode shows the most common score; the median shows that half the class scored 50 or less.

Quick revision

Mean, median and mode are averages.
Histogram bars touch; bar graph bars do not.
Mode can be more than one value.

Exam tips

Always arrange data in order before finding the median.
In histograms with unequal class widths, adjust the bar heights.

Practice MCQs

Mean of 4, 6, 8, 10 is
1. 6
2. 7
3. 8
4. 28
Show answer
Answer: (b) 7. 28/4 = 7.
The most frequent value in data is the
1. mean
2. median
3. range
4. mode
Show answer
Answer: (d) mode. Mode.
Median of 3, 7, 9, 12, 15 is
1. 9
2. 7
3. 12
4. 9.2
Show answer
Answer: (a) 9. Middle value.
Median of 2, 5, 8, 11 is
1. 5
2. 8
3. 6.5
4. 6
Show answer
Answer: (c) 6.5. (5 + 8)/2.
Range of 12, 7, 25, 18, 3 is
1. 25
2. 22
3. 13
4. 18
Show answer
Answer: (b) 22. 25 − 3.
Data you collect yourself through a survey is
1. secondary
2. false
3. grouped
4. primary
Show answer
Answer: (d) primary. Primary data.
The mean of 5 numbers is 18. If one number is removed the mean becomes 16. The removed number is
1. 24
2. 18
3. 26
4. 22
Show answer
Answer: (c) 26. 90 − 64 = 26.
Class mark of 25–35 is
1. 25
2. 30
3. 35
4. 10
Show answer
Answer: (b) 30. (25 + 35)/2.

All chapters of Class 9 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.