Mean and Median
ICSE Class 6 · Mathematics · Chapter 34
What this chapter covers
- One number for a whole set of data
- Mean (average) of data
- Median of data
- Problems on mean and median
Key points
- An observation is one value in a set of data.
- A representative value is one number that stands for a whole set of data.
- Mean = sum of all the observations ÷ number of observations; the mean is also called the average.
- The mean is the share each would get if the total were divided equally, and it is the balance point of the data.
- The mean always lies between the smallest and the largest observation, but need not be one of them.
- The median is the middle value of data arranged in ascending or descending order.
- For an odd number of observations, the median is the single middle value.
- For an even number of observations, the median is the mean of the two middle values.
- Sum of observations = mean × number of observations, which helps you find a missing value.
- One very large or very small value changes the mean a lot but hardly changes the median.
Questions answered
What is an observation? How many observations are there in the data 4, 9, 2, 7?
An observation is one value in a set of data. There are 4 observations.
Find the mean of 6, 8, 10, 12 and 14.
Sum = 50, number of observations = 5, so mean = 50 ÷ 5 = 10.
Find the median of 19, 3, 11, 7 and 15.
In order: 3, 7, 11, 15, 19. The middle (3rd) value is 11, so the median is 11.
Find the median of 5, 12, 8, 3, 10 and 6.
In order: 3, 5, 6, 8, 10, 12. The middle values are 6 and 8. Median = (6 + 8) ÷ 2 = 7.
Three friends have ₹20, ₹35 and ₹50. If they share the money equally, how much does each get? What is this amount called?
Total = ₹105, and 105 ÷ 3 = ₹35 each. This is the mean amount of money.
The mean of 6 numbers is 9. What is their sum?
Sum = 9 × 6 = 54.
The mean of four numbers is 15. Three of them are 10, 14 and 18. Find the fourth number.
Total needed = 15 × 4 = 60. Sum of the known numbers = 42. Missing number = 60 − 42 = 18.
Aman says the median of 9, 1, 4 is 1 because 1 is in the middle. Is he right?
No. The data must be arranged first: 1, 4, 9. The median is 4.