Grade 9–10 · Free math lesson

Statistics & Probability

After this lesson, you will be able to find averages, read data, and predict how likely something is to happen.

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Skills in this unit

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Standards covered:6.SP.B.5.c6.SP.B.4S-ID.A.1S-ID.A.27.SP.C.57.SP.C.77.SP.C.88.SP.A.4S-CP.A.48.SP.A.18.SP.A.2S-ID.B.6S-CP.B.9

Find the Mean (Average)

Add all the numbers together, then divide by how many numbers there are. This gives you the 'middle ground' of your data.

Example: Test scores: 70, 80, 90. Add them: 70+80+90 = 240. Divide by 3: 240÷3 = 80. The mean is 80.

Remember: Mean = Add then Divide. Remember: 'A' comes before 'D' — Add first, Divide second!

Read a Data Set

Data sets have three key values: the median (middle number), the mode (most repeated number), and the range (biggest minus smallest). These help you understand your data at a glance.

Example: Data: 3, 5, 5, 7, 9. Median = 5 (middle). Mode = 5 (appears twice). Range = 9−3 = 6.

Remember: Mode = Most Often. Both start with 'Mo' — easy to remember!

Calculate Probability

Probability tells you how likely something is to happen. Write it as a fraction: favorable outcomes ÷ total possible outcomes.

Example: A bag has 3 red and 7 blue marbles. Probability of picking red = 3÷10 = 0.3 or 30%.

Remember: Probability is always between 0 (impossible) and 1 (certain). Think of it like a percentage out of 100!

Worked example

A student rolled a die 5 times and got: 3, 5, 2, 5, 5. Find the mean, mode, and probability of rolling a 5 on a normal die.

  1. 1Step 1 — Mean: Add the rolls: 3+5+2+5+5 = 20. Divide by 5: 20÷5 = 4. The mean is 4.
  2. 2Step 2 — Mode: The number 5 appears 3 times — more than any other. The mode is 5.
  3. 3Step 3 — Probability of rolling a 5: A die has 6 sides. Only one side is 5. So probability = 1/6 ≈ 17%.

Answer: Mean = 4, Mode = 5, Probability of rolling a 5 = 1/6.

The #1 mistake to avoid

Students forget to sort the data before finding the median. Always arrange numbers from smallest to largest first, then pick the middle value!

Key takeaways

  • Mean = sum of all values ÷ number of values (the average).
  • Median is the middle value, mode is the most frequent, and range is max minus min.
  • Probability = favorable outcomes ÷ total outcomes, always between 0 and 1.

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