Statistics and probability
Showing data in tables and graphs, finding the mode, median, mean and range, and describing how likely things are.
📌 Key points
- Data can be shown in tally charts, frequency tables, pictograms, bar charts, line graphs, pie charts, Venn diagrams and Carroll diagrams.
- Line graphs show how something changes over time, such as the temperature during a day.
- The mode is the most common value. A set of data can have more than one mode.
- The median is the middle value when the data is in order. If there are two middle values, it is halfway between them.
- The mean is the total of all the values divided by how many values there are.
- The range is the largest value minus the smallest value. It shows how spread out the data is.
- Words for chance: impossible, unlikely, even chance, likely, certain.
- Probability can be shown on a scale from 0 (impossible) to 1 (certain). An even chance is 12.
- If all outcomes are equally likely, the chance of an outcome is the number of ways it can happen out of the total number of outcomes.
📖 Key words
- Data
- Information that is collected, such as numbers or answers to a question.
- Frequency
- How many times something happens or appears.
- Mode
- The most common value in a set of data.
- Median
- The middle value when the data is put in order.
- Mean
- The total of the values divided by the number of values.
- Range
- The difference between the largest and the smallest values.
- Probability
- How likely it is that something will happen.
✏️ Worked example
Find the mode, median, mean and range of these scores: 4, 7, 3, 7, 9.
- Put the data in order: 3, 4, 7, 7, 9.
- Mode = 7 (it appears twice). Median = the middle value = 7.
- Mean = (3 + 4 + 7 + 7 + 9) ÷ 5 = 30 ÷ 5 = 6.
- Range = 9 − 3 = 6.
- Answer: mode 7, median 7, mean 6, range 6.
Always put the data in order before finding the median, and count the values to make sure you have not missed one.
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