Average
We say, "I drink about 7 glasses of water a day." The number is different on each day, yet one common figure is quoted. This representative number is the average.
Add all the scores and divide the sum by how many scores there are; the result is the average. Each number in the data is called a score.
In the figure: The glasses drunk in 5 days are 6, 8, 5, 9, 7. The sum is 6 + 8 + 5 + 9 + 7 = 35. There are 5 days, so the average is 35 ÷ 5 = 7 (the red dashed line).
Rule 1: Average = sum of the scores ÷ number of scores — First add all the scores, then divide the sum by how many scores there are.
- Easy: Three scores 4, 6, 8. Sum = 4 + 6 + 8 = 18. Average = 18 ÷ 3 = 6.
- Medium: In five days a child read 12, 15, 9, 14, 10 pages. Sum = 12 + 15 + 9 + 14 + 10 = 60. Average = 60 ÷ 5 = 12 pages.
- Exam type: A team's runs in six matches are 45, 52, 38, 60, 41, 64. Sum = 45 + 52 + 38 + 60 + 41 + 64 = 300. Average = 300 ÷ 6 = 50 runs.
In the figure: The number line runs from 4 to 10. The scores 5, 6, 7, 8, 9 are shown as dots; the smallest 5 and the largest 9 are amber. The average 7 lies between them: 5 ≤ 7 ≤ 9.
Rule 2: The average always lies between the smallest and the largest score — The average is never below the smallest score or above the largest score. If it is, there is a mistake in the addition or the division.
- Easy: Scores 3, 5, 7. Average = 15 ÷ 3 = 5 and 3 ≤ 5 ≤ 7.
- Medium: Scores 20, 30, 25, 45. Sum = 20 + 30 + 25 + 45 = 120. Average = 120 ÷ 4 = 30 and 20 ≤ 30 ≤ 45.
- Exam type: Someone says the average of four scores is 18, but every score is 20 or more. That is not possible, because the average cannot be smaller than the smallest score.
In the figure: The differences of the scores 6, 8, 5, 9, 7 from the average 7 are −1, +1, −2, +2, 0. −1 + 1 − 2 + 2 + 0 = 0.
Rule 3: The differences from the average cancel each other — What the larger scores have above the average equals what the smaller scores lack, so all the differences add up to 0.
- Easy: Scores 4, 6, 8 and average 6. Differences −2, 0, +2 and −2 + 0 + 2 = 0.
- Medium: Scores 10, 14, 12, 16. Sum 52, average 13. Differences −3, +1, −1, +3 and −3 + 1 − 1 + 3 = 0.
- Exam type: The average of three scores is 10. Two scores are 7 and 11. Their differences are −3 and +1, so the third difference must be +2. Third score = 10 + 2 = 12.
Average
In the app you can move this figure with your finger.
Open in the appAverage = sum ÷ number of scores. In the figure, 35 ÷ 5 = 7.
Dividing by the wrong number without counting the scores. The figure has 5 scores, so divide by 5, not by 6.
To check the answer, see whether the average lies between the smallest and the largest score.
Spot the difference
| Point | Sum | Average |
|---|---|---|
| Value in the figure | 35 | 7 |
| How we get it | Add all the scores | Divide the sum by 5 |
| Meaning | Total glasses in 5 days | Usual glasses per day |
| If a new score is added | Always rises | Rises or falls with the score |
Practice questions
- 1Find the average of the scores 9, 11, 13, 7.
- 2The pages read each day in a week are 20, 25, 15, 30, 25, 15, 10. What is the average number of pages per day?
- 3Three friends saved 16, 24, 20 rupees. What is the average?
- 4The average of six scores is 15. The smallest score is 12 and the largest is 18. Does the average lie between them?
- 5Find the average of the scores 14, 18, 10, 22, 16, 16. How many scores are above the average?
- 6Write the differences of the scores 8, 12, 10, 14, 6 from the average 10 and check their sum.
- 7The average of four scores is 12. Three of them are 9, 15, 10. Use the differences to find the fourth score.
- 8The average over six days was 8 glasses of water. On the seventh day 15 glasses were drunk. What is the average over seven days?
Show answers (try them yourself first)
- 1Sum = 9 + 11 + 13 + 7 = 40. Average = 40 ÷ 4 = 10.
- 2Sum = 20 + 25 + 15 + 30 + 25 + 15 + 10 = 140. Average = 140 ÷ 7 = 20 pages. 3) Sum = 16 + 24 + 20 = 60. Average = 60 ÷ 3 = 20 rupees.
- 4The average is 15 and 12 ≤ 15 ≤ 18, so yes, it lies between them.
- 5Sum = 14 + 18 + 10 + 22 + 16 + 16 = 96. Average = 96 ÷ 6 = 16. The scores above 16 are 18 and 22, that is 2 scores.
- 6The average is 10. Differences 8 − 10 = −2, 12 − 10 = +2, 10 − 10 = 0, 14 − 10 = +4, 6 − 10 = −4. Sum −2 + 2 + 0 + 4 − 4 = 0.
- 7Differences 9 − 12 = −3, 15 − 12 = +3, 10 − 12 = −2. Their sum is −2, so the fourth difference is +2. Fourth score = 12 + 2 = 14.
- 8Sum for six days = 6 × 8 = 48. Sum for seven days = 48 + 15 = 63. Average = 63 ÷ 7 = 9 glasses.
Units, decimals and missing scores
If one distance from home to the market is given in km and another in metres, we cannot add them as they are. First both must be written in the same unit. 1 km = 1000 metres.
Before finding an average, write all the scores in the same unit. The average need not be a whole number; it can be a decimal. Sum of scores = average × number of scores, and this helps us find a missing score.
In the figure: Four distances are 1.2 km, 900 metres, 600 metres and 1.5 km. Changing km to metres, 1.2 became 1200 and 1.5 became 1500. The sum is 1200 + 900 + 600 + 1500 = 4200. The average is 4200 ÷ 4 = 1050 metres.
Rule 1: Bring all scores to the same unit, then add — 1 km = 1000 metres and 1 kg = 1000 grams. If the units are left different, the sum comes out wrong.
- Easy: Distances 2 km and 800 metres. In metres, 2000 + 800 = 2800. Average = 2800 ÷ 2 = 1400 metres.
- Medium: Three bags weigh 1.5 kg, 500 grams, 1 kg. In grams, 1500 + 500 + 1000 = 3000. Average = 3000 ÷ 3 = 1000 grams.
- Exam type: Distances 2.5 km, 1.5 km, 800 metres, 1200 metres. In metres, 2500 + 1500 + 800 + 1200 = 6000. Average = 6000 ÷ 4 = 1500 metres.
In the figure: 16 books are shared equally among 5 children. Each child gets 3 books and 1 is left. When that 1 is cut into five parts, each child gets 0.2. So each gets 3.2, that is 16 ÷ 5 = 3.2.
Rule 2: Even if the scores are whole numbers, the average can be a decimal — If the sum does not divide exactly by the number of scores, the average comes as a decimal. For countable things we say "about".
- Easy: Scores 3, 4, 4. Sum 11. Average = 11 ÷ 3 ≈ 3.67.
- Medium: Goals in five matches: 2, 3, 0, 4, 2. Sum = 2 + 3 + 0 + 4 + 2 = 11. Average = 11 ÷ 5 = 2.2 goals.
- Exam type: Spending over seven days: 45, 50, 38, 47, 52, 40, 46 rupees. Sum = 45 + 50 + 38 + 47 + 52 + 40 + 46 = 318. Average = 318 ÷ 7 ≈ 45.43 rupees.
In the figure: The average of 5 scores is 8, so the sum is 8 × 5 = 40. The four known scores 7, 9, 6, 9 add up to 31. The missing score (the amber ?) = 40 − 31 = 9.
Rule 3: Sum of the scores = average × number of scores — So the missing score = total sum − sum of the known scores.
- Easy: If the average of 4 scores is 5, the total sum = 5 × 4 = 20.
- Medium: The average of 3 scores is 10. Two scores are 8 and 13. Total sum = 10 × 3 = 30. Missing score = 30 − (8 + 13) = 30 − 21 = 9.
- Exam type: The average of 6 subjects is 70 marks. Five subjects have 65, 72, 80, 58, 70. Total = 70 × 6 = 420. Known = 65 + 72 + 80 + 58 + 70 = 345. Sixth = 420 − 345 = 75.
Units, decimals and missing scores
In the app you can move this figure with your finger.
Open in the appUnits, decimals and missing scores
In the app you can move this figure with your finger.
Open in the appFirst make the units the same, then add, then divide. Missing score = average × number − sum of the known scores.
Adding 1.2 km and 900 metres as they are. 1.2 + 900 means nothing; change 1.2 km to 1200 metres and then add 1200 + 900.
To find a missing score, first multiply the average by the number of scores, then subtract the known scores.
Spot the difference
| Item | Wrong | Right |
|---|---|---|
| Distances 1.2 km and 900 metres | 1.2 + 900 | 1200 + 900 |
| Answer of 16 ÷ 5 | 3 (decimal dropped) | 3.2 |
| Average 8 of 5 scores | Sum 8 + 5 = 13 | Sum 8 × 5 = 40 |
| Missing score | 31 − 40 | 40 − 31 = 9 |
Practice questions
- 1Find the average of the distances 3 km and 500 metres in metres.
- 2Find the average of the scores 5, 6, 8. (Up to two decimal places.)
- 3The average of 4 scores is 9. What is their total sum?
- 4Three bags weigh 2 kg, 600 grams and 1.6 kg. What is the average weight in grams?
- 5The average of 5 scores is 14. Four scores are 10, 12, 20, 16. What is the fifth score?
- 6The mangoes eaten in five days were 3, 4, 2, 5, 3. What is the average per day?
- 7The average of 4 scores is 15. Three of them are 12, 18, 20. What is the fourth score?
- 8The average of 6 scores is 7. The score 12 among them is removed. What is the average of the remaining 5 scores?
Show answers (try them yourself first)
- 13 km = 3000 metres. Sum = 3000 + 500 = 3500. Average = 3500 ÷ 2 = 1750 metres.
- 2Sum = 5 + 6 + 8 = 19. Average = 19 ÷ 3 ≈ 6.33. 3) Sum = 9 × 4 = 36.
- 42 kg = 2000 grams and 1.6 kg = 1600 grams. Sum = 2000 + 600 + 1600 = 4200. Average = 4200 ÷ 3 = 1400 grams.
- 5Total = 14 × 5 = 70. Known = 10 + 12 + 20 + 16 = 58. Fifth score = 70 − 58 = 12.
- 6Sum = 3 + 4 + 2 + 5 + 3 = 17. Average = 17 ÷ 5 = 3.4 mangoes.
- 7Total = 15 × 4 = 60. Known = 12 + 18 + 20 = 50. Fourth score = 60 − 50 = 10.
- 8Total = 7 × 6 = 42. After removing 12, 42 − 12 = 30. Average = 30 ÷ 5 = 6.
Frequency and tally marks
To count how many books each child in a class read, we read out the names one by one, make a mark on a slate and count the marks at the end. Tally marks make such counting easy.
The number of times a score occurs in the data is its frequency. A table with three columns, the score, tally marks and frequency, is a frequency table.
In the figure: 4 tally marks are drawn upright and the fifth is drawn across them. A group of 5 is 4 upright marks and 1 across. 12 = 5 + 5 + 2, that is two full groups and 2 marks.
Rule 1: Four upright marks and the fifth across — Groups of five make counting easy. Count each full group as 5 and count the remaining marks one by one.
- Easy: One full group is 5.
- Medium: 2 full groups and 3 marks = 5 + 5 + 3 = 13.
- Exam type: 3 full groups and 4 marks = 5 + 5 + 5 + 4 = 19.
In the figure: The data of the books taken by 20 children is in the top two rows. The first column has the scores 1, 2, 3, 4, 5, the second the tally marks and the third the frequencies 2, 5, 8, 3, 2. The total N = 20.
Rule 2: Steps to make a frequency table — Write the scores from the smallest to the largest. Read the data in order and make one mark against each. At the end count the marks and write the frequencies.
- Easy: Data 2, 1, 2, 3, 1, 2. The score 1 occurs two times, the score 2 three times and the score 3 one time.
- Medium: Data 4, 5, 4, 4, 6, 5, 4, 6, 5, 4. The score 4 occurs five times, the score 5 three times and the score 6 two times.
- Exam type: Data 1, 3, 2, 3, 3, 1, 2, 3, 4, 3, 2, 3. Frequencies: score 1 → 2, score 2 → 3, score 3 → 6, score 4 → 1.
In the figure: The frequencies of the scores 1, 2, 3, 4, 5 are 2, 5, 8, 3, 2. Their sum is 2 + 5 + 8 + 3 + 2 = 20.
Rule 3: Sum of all the frequencies N = number of scores in the data — If this sum does not equal the number of scores, there is a counting mistake.
- Easy: Frequencies 3, 4, 2. N = 3 + 4 + 2 = 9.
- Medium: In data of 15 scores the frequencies are 4, 6, 3 and a fourth that is not known. 4 + 6 + 3 = 13 and the fourth = 15 − 13 = 2.
- Exam type: The frequencies 5, 7, 9, 4 add up to 25, but the data has 26 scores. So one score was left uncounted.
Frequency and tally marks
In the app you can move this figure with your finger.
Open in the appFrequency tells how many times a score occurs. The sum of all frequencies N is the total number of scores.
Drawing a sixth upright mark instead of drawing the fifth across. Then the groups cannot be recognised and the counting goes wrong.
Read a score from the data, make its mark at once and cross the score out. At the end match the sum of the frequencies with N.
Spot the difference
| Point | Score | Frequency |
|---|---|---|
| Example in the figure | 3 | 8 |
| Meaning | A number in the data | How many times it came |
| Which column | The first | The third |
| Total | Not linked to N | Sum is N = 20 |
Practice questions
- 1How will you show 7 with tally marks?
- 2What is the frequency if there are 2 full groups and 4 marks?
- 3Data 2, 3, 3, 2, 3. How many times does 3 occur? That count is its frequency.
- 4Data 1, 2, 2, 1, 3, 2, 2, 3. Make the frequency table and state N.
- 5If the frequencies are 6, 9, 5, 4, what is N?
- 6In data of 30 scores, three frequencies are 7, 10, 8. What is the fourth frequency?
- 7The frequencies of the scores 1 to 5 are 3, 8, ?, 6, 2 and N = 30. What is the third frequency?
- 8Data 5, 3, 4, 5, 5, 2, 4, 5, 3, 4, 5, 4. Make the frequency table.
Show answers (try them yourself first)
- 1One full group of 5 and 2 marks, that is 5 + 2 = 7.
- 2Frequency = 5 + 5 + 4 = 14. 3) The score 3 occurs three times, so its frequency is 3.
- 4Score 1 → 2, score 2 → 4, score 3 → 2. N = 2 + 4 + 2 = 8.
- 5N = 6 + 9 + 5 + 4 = 24.
- 67 + 10 + 8 = 25. The fourth frequency = 30 − 25 = 5.
- 7Sum of the known = 3 + 8 + 6 + 2 = 19. The third frequency = 30 − 19 = 11.
- 8Score 2 → 1, score 3 → 2, score 4 → 4, score 5 → 5. N = 1 + 2 + 4 + 5 = 12.
Average from a frequency table
Instead of adding the books taken by 20 children one by one, we can say "five children took 2 books each" and quickly get 5 × 2 to build the sum.
In a frequency table, multiply each score by its frequency and add all the products. That is the sum of all the scores. Divide it by N to get the average.
In the figure: The scores 1 to 5 and their frequencies 2, 5, 8, 3, 2. The products are 1 × 2 = 2, 2 × 5 = 10, 3 × 8 = 24, 4 × 3 = 12, 5 × 2 = 10. The sum of the frequencies is N = 20 and the sum of the products is 58. The average is 58 ÷ 20 = 2.9.
Rule 1: Sum of (score × frequency) = sum of all the scores — Multiplying a score by its frequency gives the whole contribution of that score over all its occurrences.
- Easy: The score 2 came five times. 2 × 5 = 10, that is 2 + 2 + 2 + 2 + 2 = 10.
- Medium: The scores 1, 2, 3 have frequencies 4, 3, 2. Products 1 × 4 = 4, 2 × 3 = 6, 3 × 2 = 6. Sum = 4 + 6 + 6 = 16.
- Exam type: The scores 10, 20, 30 have frequencies 3, 5, 2. Products 10 × 3 = 30, 20 × 5 = 100, 30 × 2 = 60. Sum = 30 + 100 + 60 = 190.
Rule 2: Average = (sum of score × frequency) ÷ N — The divisor N is the sum of the frequencies, not the number of different scores.
- Easy: Scores 1, 2, 3 with frequencies 2, 4, 2. Sum = 1 × 2 + 2 × 4 + 3 × 2 = 2 + 8 + 6 = 16. N = 2 + 4 + 2 = 8. Average = 16 ÷ 8 = 2.
- Medium: Scores 5, 6, 7 with frequencies 3, 4, 3. Sum = 5 × 3 + 6 × 4 + 7 × 3 = 15 + 24 + 21 = 60. N = 10. Average = 60 ÷ 10 = 6.
- Exam type: Scores 0, 1, 2, 3 with frequencies 5, 8, 4, 3. Sum = 0 × 5 + 1 × 8 + 2 × 4 + 3 × 3 = 0 + 8 + 8 + 9 = 25. N = 20. Average = 25 ÷ 20 = 1.25.
In the figure: The number line shows 1, 2, 3, 4, 5, and a red arrow marks the average 2.9. 1 ≤ 2.9 ≤ 5.
Rule 3: The average need not be a score in the table — It lies between the smallest and the largest score, but it need not be one of the scores in the table.
- Easy: If the scores are 1 to 5, the average lies between 1 and 5, for example 2.9.
- Medium: If the scores are 3 to 7 and the average comes as 2, it is wrong, because 2 < 3.
- Exam type: The scores are 1 to 5 and the average comes as 6. 6 > 5, so the sum or N is wrong.
Average from a frequency table
In the app you can move this figure with your finger.
Open in the appAverage = (sum of score × frequency) ÷ N. In the figure, 58 ÷ 20 = 2.9.
Dividing by the number of different scores instead of N. In the figure it is 58 ÷ 20, not 58 ÷ 5.
Add a third column to the table, score × frequency, and add it up.
Spot the difference
| Point | N | Sum of the products |
|---|---|---|
| Value in the figure | 20 | 58 |
| Sum of what | The frequencies | Score × frequency |
| In the division | The divisor | The dividend |
| In 58 ÷ 20 | 20 | 58 |
Practice questions
- 1The score 3 came six times. What is its product?
- 2Scores 1, 2 with frequencies 3, 3. What is the average?
- 3If the frequencies are 4, 5, 6, what is N?
- 4Scores 2, 3, 4 with frequencies 5, 10, 5. What is the average?
- 5Scores 10, 20, 30, 40 with frequencies 2, 3, 4, 1. What is the average?
- 6Scores 0, 1, 2 with frequencies 6, 3, 1. What is the average?
- 7The scores 1, 2, 3, 4 have frequencies 3, ?, 4, 1 and N = 12. What is the average?
- 8A table has N = 25 and average 3.2. What is the sum of all the scores?
Show answers (try them yourself first)
- 1Product = 3 × 6 = 18.
- 2Sum = 1 × 3 + 2 × 3 = 3 + 6 = 9. N = 3 + 3 = 6. Average = 9 ÷ 6 = 1.5. 3) N = 4 + 5 + 6 = 15.
- 4Sum = 2 × 5 + 3 × 10 + 4 × 5 = 10 + 30 + 20 = 60. N = 5 + 10 + 5 = 20. Average = 60 ÷ 20 = 3.
- 5Sum = 10 × 2 + 20 × 3 + 30 × 4 + 40 × 1 = 20 + 60 + 120 + 40 = 240. N = 2 + 3 + 4 + 1 = 10. Average = 240 ÷ 10 = 24.
- 6Sum = 0 × 6 + 1 × 3 + 2 × 1 = 0 + 3 + 2 = 5. N = 6 + 3 + 1 = 10. Average = 5 ÷ 10 = 0.5.
- 7Second frequency = 12 − (3 + 4 + 1) = 12 − 8 = 4. Sum = 1 × 3 + 2 × 4 + 3 × 4 + 4 × 1 = 3 + 8 + 12 + 4 = 27. Average = 27 ÷ 12 = 2.25.
- 8Sum = 3.2 × 25 = 80.
Averages in daily life
We hear of a batter's average in cricket, the average rainfall of a month and the average daily sales of a shop. An average gives a simple picture of many numbers.
An average is one representative number for a group. It lets us compare two groups. But one very large or very small score pulls the average towards itself.
In the figure: The spending is 40, 45, 35, 40 and one big score 100. The average of the first four is 160 ÷ 4 = 40 (green line). All five together give 260 ÷ 5 = 52 (red line).
Rule 1: One extreme score pulls the average towards itself — So when you look at an average, check whether the data has one very different score.
- Easy: The scores 10, 10, 10 add up to 30. Now 40 comes in: (30 + 40) ÷ 4 = 70 ÷ 4 = 17.5.
- Medium: The scores 21, 25, 17, 21 add up to 84 and the average is 21. Add the score 3: (84 + 3) ÷ 5 = 87 ÷ 5 = 17.4. The average came down.
- Exam type: The average of 5 scores is 30, so the sum is 150. If the sixth score is 30, (150 + 30) ÷ 6 = 180 ÷ 6 = 30, so the average stays the same. If the sixth score is 36, (150 + 36) ÷ 6 = 186 ÷ 6 = 31.
In the figure: In the top row there are 5 children with 8 sheets each, a total of 5 × 8 = 40. In the bottom row there are 8 children with 7 each, a total of 8 × 7 = 56. The bottom row has the larger total, but the top row has the larger average per child: 8 > 7.
Rule 2: Compare two groups by the average, not by the total — If the groups have different numbers of members, the total misleads. Find total ÷ number for each group and then compare.
- Easy: In the first group 20 children saved 100 rupees in all, and in the second 10 children saved 60 rupees. 100 ÷ 20 = 5 and 60 ÷ 10 = 6. The second group has the larger average.
- Medium: The first team made 120 runs in 4 matches and the second made 125 runs in 5 matches. 120 ÷ 4 = 30 and 125 ÷ 5 = 25. The first team has the larger average.
- Exam type: The first family spent 420 rupees in 6 days and the second 320 rupees in 4 days. 420 ÷ 6 = 70 and 320 ÷ 4 = 80. The second family spends more per day.
Rule 3: An average is not everyone's real score — It need not be anybody's actual score. For countable things we say "about".
- Easy: An average of 2.9 books does not mean anyone took 2.9 books; it is about 3 books.
- Medium: An average of 4.2 people per house in a village means about 4 people.
- Exam type: 37 people live in 10 houses. 37 ÷ 10 = 3.7, so there are about 4 people per house.
Averages in daily life
In the app you can move this figure with your finger.
Open in the appAn average gives a simple picture of a group. When comparing two groups, look at the average instead of the total.
Comparing totals when the groups have different numbers of children. In the figure 56 > 40, but the average 7 < 8.
First find total ÷ number for each group, then compare the averages.
Spot the difference
| Point | Total | Average |
|---|---|---|
| Top row (figure) | 40 | 8 |
| Bottom row (figure) | 56 | 7 |
| Which is larger | The bottom | The top |
| For comparing | Wrong, numbers differ | Right, divided by the number |
Practice questions
- 1The heights of 5 children are 140, 150, 145, 155, 160 cm. What is the average height?
- 2Three sacks weigh 48, 50, 52 kg. What is the average weight?
- 3The total rainfall in 6 days is 90 mm. What is the average per day?
- 4The scores are 30, 32, 28, 30. The score 90 is added. What is the new average?
- 5In the first group 8 children have 96 sheets in all, and in the second 12 children have 120 sheets in all. Which group has the larger average?
- 6There are 43 people in 10 houses. What is the average per house, and about how many?
- 7The average sales over 4 days was 500 rupees. On the fifth day the sales were 750 rupees. What is the average over five days?
- 8The average of 5 scores was 24. A sixth score 12 is added. What is the new average?
Show answers (try them yourself first)
- 1Sum = 140 + 150 + 145 + 155 + 160 = 750. Average = 750 ÷ 5 = 150 cm.
- 2Sum = 48 + 50 + 52 = 150. Average = 150 ÷ 3 = 50 kg. 3) Average = 90 ÷ 6 = 15 mm.
- 4Sum of the four scores = 30 + 32 + 28 + 30 = 120. New average = (120 + 90) ÷ 5 = 210 ÷ 5 = 42.
- 5First group 96 ÷ 8 = 12. Second group 120 ÷ 12 = 10. The first group has the larger average.
- 6Average = 43 ÷ 10 = 4.3, that is about 4 people per house.
- 7Sum for four days = 500 × 4 = 2000. For five days = 2000 + 750 = 2750. Average = 2750 ÷ 5 = 550 rupees.
- 8First sum = 24 × 5 = 120. New average = (120 + 12) ÷ 6 = 132 ÷ 6 = 22.