Average
Average
Key Concepts
- Average usually means the mean in PSLE questions.
- The mean/average tells us the equal share for a set of values.
- Example: If 4 children share 20 sweets equally, each gets 5 sweets. So the average is 5.
- To find the average:
- Add up all the values.
- Divide by the number of values.
Formula for Average
- Average = Total ÷ Number of items
- You must know:
- Total = sum of all the values
- Number of items = how many values there are
Rearranging the Formula
Sometimes the average is given, and you need to find the total.
- Total = Average × Number of items
If one value is missing:
- Find the total using
Total = Average × Number of items - Add up the known values.
- Subtract from the total to find the missing value.
Understanding What Average Means
- The average does not always have to be one of the actual values.
- The average can be:
- a whole number
- a decimal
- a value smaller than some numbers and larger than others
- The average helps us compare groups fairly.
Average in Word Problems
In word problems, the values may represent:
- marks
- heights
- masses
- number of books read
- money saved
- temperatures
- distances
To solve word problems:
- Identify the number of items.
- Find the total or average needed.
- Use the correct formula.
- Check whether the answer makes sense.
Comparing Averages
When comparing two or more groups:
- Find the average for each group first.
- Then compare the averages.
- A higher average means the group has a greater equal-share value.
Be careful:
- A group with a larger total does not always have a larger average.
- The number of items matters too.
Example:
- Group A: total 40 from 5 people → average 8
- Group B: total 42 from 7 people → average 6
Even though 42 is more than 40, Group B has a smaller average.
Useful Thinking Method
For average questions, ask:
- What is the total?
- How many items are there?
- Is there a missing value?
- Am I asked to compare two groups?
Important Definitions
- Average (Mean): the total of all the values divided by the number of values.
- Total: the sum of all the values.
- Number of items: the number of values in the group.
- Missing value: a value that is not given and must be found using the average or total.
- Compare: to look at two or more values and decide which is greater, smaller, or if they are equal.
- Word problem: a question written in sentences that describes a real-life situation using numbers.
Worked Examples
Example 1: Calculating Mean/Average
The masses of 4 durians are 2 kg, 3 kg, 4 kg and 5 kg. Find the average mass.
Step 1: Find the total mass
- 2 + 3 + 4 + 5 = 14 kg
Step 2: Count the number of durians
- There are 4 durians.
Step 3: Use the formula
- Average = Total ÷ Number of items
- Average = 14 ÷ 4
- Average = 3.5 kg
Answer
- The average mass is 3.5 kg.
Example 2: Finding a Missing Value Given the Average
The average score of 5 pupils is 72. Four of the scores are 68, 70, 75 and 74. Find the fifth score.
Step 1: Find the total score
- Total = Average × Number of items
- Total = 72 × 5
- Total = 360
Step 2: Add the 4 known scores
- 68 + 70 + 75 + 74 = 287
Step 3: Find the missing score
- Missing score = Total - Sum of known scores
- Missing score = 360 - 287
- Missing score = 73
Answer
- The fifth score is 73.
Check
- 68 + 70 + 75 + 74 + 73 = 360
- 360 ÷ 5 = 72 ✔
Example 3: Comparing Averages
Class A collected 48 cans over 6 days.
Class B collected 56 cans over 8 days.
Which class collected more cans on average per day?
Step 1: Find Class A’s average
- Average = 48 ÷ 6
- Average = 8 cans per day
Step 2: Find Class B’s average
- Average = 56 ÷ 8
- Average = 7 cans per day
Step 3: Compare
- 8 > 7
Answer
- Class A collected more cans on average per day.
Common Mistakes to Avoid
- Forgetting to divide by the number of items.
- Dividing by the wrong number.
- Example: using 4 instead of 5 when there are 5 values.
- Mixing up the formulas:
- Average = Total ÷ Number of items
- Total = Average × Number of items
- Finding the total correctly but forgetting to subtract the known values when finding a missing value.
- Adding wrongly when finding the total.
- Comparing totals instead of comparing averages.
- Forgetting units in the final answer.
- Example: cm, kg, marks, cans per day
- Writing an answer that does not make sense in the context.
- Example: a negative score or impossible mass
- Not checking if the average lies reasonably between the smallest and largest values.
- Ignoring key words such as:
- “each”
- “on average”
- “per day”
- “for all”
- “altogether”
Exam Tips
- Underline important information:
- total
- average
- number of items
- missing value
- Memorise these two formulas:
- Average = Total ÷ Number of items
- Total = Average × Number of items
- If one value is missing, always:
- find the total first
- subtract the known values
- For comparison questions:
- calculate both averages
- then state clearly which is greater
- Include units in the answer.
- Example: 7 kg, 68 marks, 5 books per week
- Show working clearly:
- this helps you earn method marks
- After solving, do a quick check:
- multiply the average by the number of items to see if it gives the total
- If the question asks “how many more on average”, subtract the two averages.
- Useful answer phrases:
- “The total is…”
- “The average is…”
- “Therefore, the missing value is…”
- “Hence, Group A has the higher average.”
Quick Summary
- Average usually means mean.
- Average = Total ÷ Number of items.
- Total = Average × Number of items.
- To find a missing value, find the total first, then subtract the known values.
- The average is an equal-share value.
- The average does not need to be one of the actual values.
- Count the number of items carefully before dividing.
- In word problems, identify whether you are given the total, average, or missing value.
- To compare groups fairly, compare their averages, not just their totals.
- Always include the correct unit in your final answer.
- Check that your answer is reasonable.
- Show clear step-by-step working in exams.
The average length of Ribbon A and B is 48 cm. The total length of Ribbon C and D is 56 cm. What is the average length of the 4 pieces of ribbon?
A player has to play a total of four games in Round 1 of a competition. The scores for Ahmad's first three games are shown below. Ahmad will qualify for Round 2 if his average score for three of the four games is 32 or more. What is the lowest score Ahmad must get in the 4th game to qualify for Round 2?
What was the average number of mini tarts sold from Monday to Friday?
The average number of mini tarts sold on Saturday and Sunday was 26 more than the average number of mini tarts sold from Monday to Friday. Write down one possible set of values for the number of mini tarts sold on Saturday and Sunday.
9 pupils took turns to play 6 Rubik's cubes during a 30-min recess. At any one time, 6 pupils played the cubes while the other 3 waited. Each had the same amount of playing time. How many minutes did each pupil play on the Rubik's cube?
Ben and Kai cycled in three races in a tournament. Their cycling times for the races are shown in the table below. Both calculated their average cycling time for the three races. Who had a faster average cycling time? What was his average cycling time?
The table below shows the different amounts of money donated by a group of students. Part of the table is covered by an ink blot. 3/4 of the group of students donated at least $5. Each statement below is either true, false or not possible to tell from the information given. For each statement, put a tick (✓) in the correct column.
The bar graph below shows the amount of money ABC clothing store earned from Monday to Thursday. What is the average amount of money ABC clothing store earned from Monday to Thursday?
The product of two numbers is 55. One of the numbers is 5. Find the average of the two numbers.
The average height of the 5 girls is more than Jane's height but less than Siti's height.
The average height of a group of children was 129.6 cm. One of the children's height was wrongly recorded as 162 cm when it should have been 126 cm. As a result, the average height calculated became 132.6 cm. How many children were there in the group?
She draws a fourth card and the average of the 4 numbers is 20. What is the number on the fourth card?
The following table shows the time taken by four students to complete a Mathematics test. One of the recorded data is covered by an ink blot. The average time taken by the four students was 72 minutes. What was the time taken by Anna to complete the test?
The average number of cups of tea sold per month from June to September was 845. How many cups of tea were sold in September?
Halim's result slip was accidentally torn. His average mark for 4 subjects is 78. Part of his Mathematics and Science marks are missing. What is the greatest possible difference between Halim's Mathematics and Science mark?
Ji Min saved some money in April. She saved $2.50 per day for 20 days. She then saved $3.10 per day for the rest of the month. What was the average amount of money she saved per day in April? (There are 30 days in April.)
Four towns A, B, C and D collected plastic bottles to be recycled. Town A and B collected an average of 324 plastic bottles. Town B, C and D collected an average of 344 plastic bottles. The total number of plastic bottles collected by all 4 towns was 6 times the number that town B collected. How many plastic bottles did town B collect?
Norman's daily allowances for a particular week are shown in the table below. Day: Mon, Tue, Wed, Thur, Fri, Sat, Sun Amount ($): 8, 10, 5, 5, 6, 5, 0 Find his average daily allowance for the week.
The actual average income of a group of adults was $3150. When Ms Tan recorded the income of these adults, she wrongly keyed in one adult's income as $2400 when it should have been $4200. As a result, Ms Tan calculated the average income as $3100. How many adults were there in the group?
Find the average of 17 and 28.
How much did Aisha save in February?
The table below shows A, B and C which represent three 2-digit numbers. Lydia used two pieces of paper to cover two of the digits in the table. The average of these 3 numbers is 25. What number is represented by C?
How many curry buns and sugar buns did Ms Noraini bake altogether?
Find the average of 5, 11 and 23.
A class of 25 students were each offered a box of donuts to sell during a fun fair. 3 of the students could not sell any of the donuts so they passed their boxes of donuts to the rest of the classmates to sell. As a result, each of the remaining students had to sell 6 more donuts. How many donuts were there in each box at first?
How many Primary 6 pupils are there?
John received the following test results from the school. What did John get for his Chinese Language marks if the average marks for all four subjects is 75?
Wynona wrote the numbers below: 20, 15, 10, 0, 10. What is the average of all the numbers?
The average age of 3 dogs was 12 years old. The age of each dog was different. The youngest dog was 8 years old. Which one of the following was a possible age of the oldest dog?
Ella wrote her composition in 45 minutes. Fandi completed his composition 5 minutes faster than Ella. Ella wrote an average of 24 words per minute. Their compositions had a total of 2000 words. What was the average number of words Fandi wrote per minute?
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