Data Organization & Analysis

Data Organization

Statistics is a way to organize scattered data into tables and graphs so you can take in the whole picture at a glance. Grouping data into intervals and counting how many fall in each gives a frequency table; drawn as bars it becomes a histogram, and joining the midpoints of the bar tops makes a frequency polygon. Relative frequency, the share of the total, lets you fairly compare two classes of different sizes, while class marks let you estimate the mean. Here you can change the class width with a slider to watch how the shape of the distribution and the mean shift.

Intuition — organize our class's scores

Bin width10pts

📊 Use Our Class's Math Scores

①Suppose we have 30 students' scores

②Divide scores into bins (classes) — e.g. 40–50, 50–60…

③Count how many students fall in each bin → frequency table

④Plot as bars → histogram

⑤Change bin width with the slider — the shape changes!

Terms in a Frequency Table

Class Mark

(endpoints sum)2

Representative value of each class. E.g. 60–70 → 65

🔍 Five Key Terms

①Variate: a data value (each student's score)

②Class: an interval grouping the data (60–70)

③Frequency: how many fall into a class

④Class width: bin size (10 pts here)

⑤Class mark: midpoint of the class (65)

Relative Frequency & Pie Chart

Relative Frequency

frequencytotal

Proportion within the total. Sum is always 1

💡 Why Relative Frequency?

①Our class has 30, the other has 35 — counts aren't directly comparable

②Convert to ratios for fair comparison

③E.g. our class score ≥ 80: 0.4 (40%); other class: 0.34 (34%)

Mean from a Frequency Distribution

Mean from a Distribution

Σ(class mark × freq)total

Approximate using class marks when raw data isn't available

📝 Histogram vs Polygon

①Histogram: bar chart with adjacent bars (continuous data)

②Polygon: connect the midpoints of bar tops with line segments

③Area enclosed is the same

④The polygon is convenient for overlaying two classes' distributions

Work It Out

Example 1

Find the mean of the data 4, 6, 8, 10, 7.

Mean = (sum of data) ÷ (number of data).

(4 + 6 + 8 + 10 + 7) ÷ 5

Compute.

= 35 ÷ 5 = 7

▸ 7

The mean adds all data and divides by the count.

Example 2

In data with total frequency 20, a class has frequency 5. Find its relative frequency.

Relative frequency = (class frequency) ÷ (total frequency).

relative frequency = 5 ÷ 20

Compute.

= 0.25

▸ 0.25

Relative frequencies always sum to 1.

Exam Key Points

Key Statistics Formulas

fN, Σ(m × f)N

Memorize these two and you're set

Grade-7 school exam type

The mean of the four numbers 3, 7, x, 10 is 7. What is x?

①6

②7

③8

④9

⑤10

▸ ③ 8

Set up the equation from the definition of mean.

(3 + 7 + x + 10) ÷ 4 = 7

Multiply both sides by 4 and solve for x.

20 + x = 28 ⇒ x = 8

🎯 Exam Key Points

①Class mark = (sum of endpoints)/2

②Σ relative frequency = 1 (always!)

③Histogram area = total count × class width

④Class with largest frequency = modal class

⑤The mean from a distribution is approximate (may differ slightly from raw data)

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