Data Handling — Class 7 IMO

Mean, Median, Mode & Range

Measures of Center describe the typical value in a dataset.

Measure	Definition	Example: {2,4,4,6,9}
Mean	Sum divided by count	(2+4+4+6+9)=25 / 5 = 5
Median	Middle value when data is sorted	Sorted: 2,4,4,6,9 — Middle = 4
Mode	Most frequently occurring value	4 appears twice — Mode = 4
Range	Maximum minus minimum	9 - 2 = 7

When dataset has even count: Median = average of the two middle values.

Outliers affect the mean significantly but not the median.

FINDING MEDIAN:

Odd dataset: {2, 4, 4, 6, 9}
  Sorted: 2  4  [4]  6  9
                 ^
              Median = 4 (3rd of 5)

Even dataset: {2, 4, 6, 8}
  Sorted: 2  [4  6]  8
               ^
         Median = (4+6)/2 = 5

MEAN as balance point:
  Data: {2, 4, 4, 6, 9}  Mean=5
  Deviations: -3, -1, -1, +1, +4
  Sum of deviations = 0 (always!)

Example 1: For 3, 5, 7, 5, 9, find the mode and the range.

Mode = 5 (appears most); range = 9 − 3 = 6.

Example 2: Find the median of 2, 4, 6, 8, 10.

The middle value is 6.

Example 3: Find mean, median, mode, range: {7, 3, 8, 3, 9, 6}

Sorted: 3,3,6,7,8,9. Mean=36/6=6. Median=(6+7)/2=6.5. Mode=3 (appears twice). Range=9-3=6.

Example 4: Test scores: 85,90,78,92,88. A new score of 65 is added. What is the new mean?

Old sum=433. New sum=433+65=498. New mean=498/6=83.

Example 5: Set {5,7,9,11,x} has a mean of 10. Find x.

(5+7+9+11+x)/5 = 10 => 32+x = 50 => x = 18.

Quick recap

Mean = sum ÷ count; median = middle value; mode = most frequent.
Range = highest − lowest.
Mean is sensitive to outliers (extreme values)
Median is resistant to outliers
Mode is the most frequent value; a dataset can have no mode or multiple modes
Range measures spread (not center)

✓ Quick check

What is the range of 4, 9, 2, 7?

Range = 9 − 2 = 7.

What is the mode of 2, 3, 3, 4?

3 appears most often.

Bar Graphs & Double Bar Graphs

A bar graph shows data with bars whose heights give the values. A double bar graph places two bars side by side for each item, so two sets of data can be compared directly.

Example 1: What does a double bar graph let us do?

Compare two sets of data side by side.

Example 2: If one bar is 30 and another is 20, what is the difference?

30 − 20 = 10.

Quick recap

Bar height shows the value; the tallest is the most.
A double bar graph compares two data sets.

✓ Quick check

Bar A is 30 and bar B is 20. What is the difference?

30 − 20 = 10.

A double bar graph compares ___ ?

It compares two sets of data.

Probability

Probability measures the chance of an event, from 0 (impossible) to 1 (certain). It is found by P = (favourable outcomes) ÷ (total outcomes). A fair coin gives P(head) = ½.

Example 1: What is the probability of getting a head on a fair coin?

1 favourable out of 2 outcomes, so ½.

Example 2: What is the probability of a certain event?

1.

Quick recap

Probability ranges from 0 (impossible) to 1 (certain).
P = favourable outcomes ÷ total outcomes.

✓ Quick check

The probability of an impossible event is ___ ?

An impossible event has probability 0.

What is the probability of rolling a 3 on a fair die?

1 favourable out of 6 outcomes, so 1/6.