Mean and median
Two familiar measures
The mean is the sum of the values divided by how many there are.
📚 Chapter Learning Kit
Tales by Dots and Lines · Class 8 Mathematics · Ganita Prakash
English 3 topics 105 leveled MCQs 51 flashcards 5 games Free
Shared by a Veda teacher · Generated with Veda AI · Oct 2026
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Halfway, at least here
Start with two numbers
Three and 7 average to 5, and 8 and 9 average to 8.5.
Not the midpoint of the extremes
The guess that fails
Two numbers make the mean look like the midpoint between the smallest and largest.
Counts, not distances
What the median answers to
The median is the middle value once the data is sorted, with as many below as above.
The middle has to shift
Adding a value above it
A set with median 8 gains the value 11, which is above the old median.
An even count has no single middle
Where it lands
The median is then the average of the two middle values.
📖 Smart notes
What you'll study, topic by topic
1
The mean as a balance point
The mean is not the midpoint between the extremes. It is the one place where the distances below it and the distances above it come to the same total.
- The mean is the total divided by the number of values.
- For two numbers the mean lies exactly halfway between them.
- For more values it is not the midpoint of the extremes.
~35 min · full explanation, examples & memory tricks in the app
2
Median, frequencies, and finding an unknown
The median answers to counts rather than to distances, so it moves differently from the mean. And a mean can be run backwards to recover a value nobody wrote down.
- The median is the middle value once the data is sorted.
- An equal number of values lie below it and above it.
- A new value above the median raises it.
~40 min · full explanation, examples & memory tricks in the app
3
Line graphs, and reading data honestly
A line graph shows how a quantity moves over time. Reading one properly means two separate steps: first setting down what is given, and only then saying what it means.
- A line graph joins points to show change over time.
- Reading one has two steps: identify, then infer.
- The first step records the axes, the scale and the series.
~35 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
105 questions laddered from warm-up to topper-level, each with an explanation. A taste:
The mean of some data is found by adding all its values and then
Beginner
A dividing the total by the largest value
B dividing the total by two and no more
C subtracting the smallest of the values
D dividing by how many values there are
Show answer & explanation
dividing by how many values there are
The median is the middle value once sorted instead.
Taking the two numbers 3 and 7 and then the two numbers 8 and 9, their means come to
Beginner
A 5 and 8
B 5 and 8.5
C 4 and 8.5
D 10 and 17
Show answer & explanation
5 and 8.5
Ten over 2, and 17 over 2.
Drawn as dots on a line, the mean of just TWO numbers always sits
Beginner
A closer to the smaller one
B exactly halfway between them
C closer to the larger one
D outside the pair
Show answer & explanation
exactly halfway between them
Which is what makes the next step so tempting.
A pupil concludes from that pair of examples that the mean is always the midpoint between the smallest and largest value, which is
Intermediate
A wrong as soon as there are three values
B right for any number of values
C right only when all the values are even
D wrong even for two values
Show answer & explanation
wrong as soon as there are three values
Two values is the one case where it happens to hold.
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