Range, and how the mean changes: Class 9 practice
Range = largest − smallest value. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Mean
The idea behind range, and how the mean changes
Range = largest − smallest value. If every observation increases by k, the mean increases by k; if every observation is multiplied by k, the mean is multiplied by k. A missing value can be found from the mean: sum = mean × n.
Step-by-step method
- Range = max − min.
- Sum = mean × number of values.
- Use the change rules for adding or multiplying all values.
Worked example 1 (Basic)
Find the range of 29, 41, 15, 30, 45, 31.
- Max 45, min 15
- Range = 30
- Answer: 30
Worked example 2 (Standard)
The mean of 6 numbers is 28. 5 of them are 21, 58, 23, 54, 33. Find the missing number.
- Total = 28 × 6 = 168
- Missing = 168 − 189 = -21
- Answer: -21
Worked example 3 (Challenge)
The mean of 18, 54, 39, 26 is 34.25. If each value is increased by 6, what is the new mean?
- Adding 6 to every value adds 6 to the mean
- = 40.25
- Answer: 40.25
Common mistakes and misconceptions
- Range as max + min
- Changing the mean by k for a single new value
Practice questions
- (Basic) Find the range of 11, 54, 21, 28, 58, 54.
- (Basic) Find the range of 16, 36, 45, 31, 54.
- (Standard) The mean of 7 numbers is 42. 6 of them are 16, 16, 11, 34, 16, 39. Find the missing number.
- (Standard) The mean of 5 numbers is 22. 4 of them are 53, 47, 35, 47. Find the missing number.
- (Challenge) The mean of 54, 30, 26, 53, 19 is 36.4. If each value is increased by 8, what is the new mean?
- (Challenge) The mean of 40, 60, 11, 16, 19, 12 is 26.33. If each value is increased by 7, what is the new mean?
Answer key with full working
- Q1: Max 58, min 11 → Range = 47 → Answer: 47
- Q2: Max 54, min 16 → Range = 38 → Answer: 38
- Q3: Total = 42 × 7 = 294 → Missing = 294 − 132 = 162 → Answer: 162
- Q4: Total = 22 × 5 = 110 → Missing = 110 − 182 = -72 → Answer: -72
- Q5: Adding 8 to every value adds 8 to the mean → = 44.4 → Answer: 44.4
- Q6: Adding 7 to every value adds 7 to the mean → = 33.33 → Answer: 33.33
Syllabus note
This skill is listed under "Statistics" for Class 9 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is range, and how the mean changes in?
"Statistics", Class 9 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.