How to Calculate the Mean (Average): Formula and Examples

To calculate the mean (average), use Mean = Sum of All Data ÷ Number of Data. Example: test scores 80, 90, and 70 → mean = (80 + 90 + 70) ÷ 3 = 240 ÷ 3 = 80. The same formula works for average report-card scores, heights, or pocket money.

What Is the Mean?

The mean (average) is a value that represents a set of data, found by adding all the data and dividing by how many there are. The mean is one measure of central tendency, alongside the median (middle value) and mode (most frequent value).

In the Indonesian curriculum, the mean is introduced in primary school and developed in middle school as part of basic statistics.

The Mean Formula

From this we can derive a formula useful for finding a missing value:

Worked Examples

Example 1: Average Score ⭐

Dani's test scores: 70, 80, 75, 85, 90. What is the mean?

• Sum = 70 + 80 + 75 + 85 + 90 = 400
• Number of data = 5
• Mean = 400 ÷ 5 = 80

Example 2: Finding a Missing Value ⭐⭐

The mean of 4 scores is 85. Three are known: 80, 90, 88. What is the fourth?

• Sum of all data = 85 × 4 = 340
• Three values = 80 + 90 + 88 = 258
• Fourth value = 340 − 258 = 82

Example 3: Combined Mean ⭐⭐⭐

Class A (20 pupils) has a mean of 75. Class B (30 pupils) has a mean of 85. What is the combined mean?

✅ The combined mean = 81 (not simply (75 + 85) ÷ 2 = 80, because the class sizes differ).

The Combined Mean Formula

When combining two groups with different sizes:

💡 Remember: You cannot find the combined mean by averaging two means when the groups have different sizes.

Mean vs Median vs Mode

• Mean: sum of data ÷ number of data.
• Median: the middle value once data is ordered.
• Mode: the most frequently occurring value.

Example data: 70, 80, 80, 90, 100.

• Mean = 420 ÷ 5 = 84
• Median = 80 (middle value)
• Mode = 80 (most frequent)

Common Mistakes When Calculating the Mean

Three mistakes pupils make most often:

• Miscounting the number of data. Make sure you divide by the COUNT of data, not the largest value or another number. 5 values → divide by 5.
• Averaging two means directly. For a combined mean, you cannot just add two means and divide by 2 if the group sizes differ — use the weighted formula.
• Forgetting zero values. A 0 still counts as one data point. E.g. 0, 80, 100 → mean = 180 ÷ 3 = 60, not 90.

💡 Quick check: the mean always lies between the smallest and largest value. If your result is outside that range, there is a calculation error.

Practice Problems

⭐ Problem 1 (Easy): Heights of 4 children: 130, 135, 140, 135 cm. What is the mean?

⭐⭐ Problem 2 (Medium): The mean of 5 scores is 78. Four are: 75, 80, 82, 70. What is the fifth?

⭐⭐⭐ Problem 3 (Challenge): Class A (15 pupils) mean 80, Class B (25 pupils) mean 88. What is the combined mean?

Answer Key:

1. (130 + 135 + 140 + 135) ÷ 4 = 540 ÷ 4 = 135 cm.
2. Sum = 78 × 5 = 390. Four values = 307. Fifth = 390 − 307 = 83.
3. ((15 × 80) + (25 × 88)) ÷ 40 = (1200 + 2200) ÷ 40 = 3400 ÷ 40 = 85.

Summary

1. Mean = Sum of All Data ÷ Number of Data.
2. To find a missing value: Sum = Mean × Number of Data.
3. The combined mean weights each group by its size — not a simple average of two means.
4. Mean, median, and mode are three different measures of central tendency.

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