Key Statistics and Probability Vocabulary IGCSE Maths Students Need To Know
If you’re an IGCSE student, you may well be feeling overwhelmed by the seemingly never-ending list of rules, terms, and formulae to learn.
The tough truth is that if they are mentioned in the official exam syllabus then you need to remember them. There’s no easy way out!
When it comes to IGCSE Maths, the place to start when learning definitions and formulae is to make sure you understand WHAT you are calculating and WHY.
To see the full set of Save My Exams Maths IGCSE Statistics and Probability Revision Videos, head here
Once you’ve read this piece and you’re ready to test your knowledge, try the Topic Questions here
The mean of a data set can be calculated by adding together all of the values and dividing the total by the number of values in the set.
In the above data set, we can see that 17 students own 1 pet, 23 students own 2 pets, etc.
The total number of students is 66, and the total number of pets owned is ((1×17)+(2×23)+(3×11)+(4×6)+(5×9))= 165
Therefore the mean number of pets is 165 / 66 = 2.5
The median value in a data set is the ‘middle’ value (when the values are in order from smallest to greatest).
Use the formula 0.5 x (n+1)th term.
In this example, because there are a total of 66 values, the ‘middle’ value is the 33.5th (0.5 x (66+1)). This means we need to calculate the number which is halfway between the 33rd and 34th value.
We can see that both the 33rd and 34th value would fall in the ‘2 pets’ group, so 2 pets is the median value.
This is the easiest average to calculate! The mode value is the most frequently occurring value – 2 pets in the above example.
The range of a data set is the difference between the smallest and the greatest value.
The range can be calculated by subtracting the smallest value from the largest value.
In the above example, the range is 4 (5-1).
The IQR can tell you how ‘spread-out’ your data is (a higher IQR = the data is more spread out between the maximum and minimum)
- To find the 1st Quartile – 0.25 x (n+1)th term
- The 2nd Quartile is equivalent to the median
- To find the 3rd Quartile 0.75 x (n+1)th term
To find IQR, calculate Q3 – Q1
In the above example, Q1 is between the 16th and 17th value (1 pet) and Q3 is between the 50th and 51st value (3 pets), so the IQR is 2.
For more on this topic, check out our Revision Video on Median, IQR, Mode, and Range
Two events are independent if one event occurring (or not) does not affect the likelihood of the other occurring. For example, if I had a bag with blue and yellow counters in it, and I was pulling out one counter at a time (and replacing the counter each time), the probability of pulling out a blue counter the second time would be independent of the colour of the counter pulled out the first time.
Conditional Probability and Dependent Events:
Conditional probability is the probability of an event occurring when the outcome depends on a previous event.
For example, the probability of it raining on any given morning is 30%.
If it rains, there is a 75% chance that my brother will take the bus to school, and if it does not rain there is a 10% chance he will take the bus.
This means that the probability of my brother taking the bus is conditional, as it is dependent on the weather conditions.
Going back to my bag with blue and yellow counters in it, if I don’t replace the first counter I pull out, then the probability of pulling out a blue counter the second time changes and is dependent on the colour of the first counter. The probability of pulling a blue counter second time is therefore a conditional probability.
Mutually Exclusive Events:
The probability of mutually exclusive events occurring simultaneously is 0.
For example, if I’m picking counters out of a bag one at a time, I can’t pick up a blue AND a yellow counter simultaneously. Additionally, weather events like ‘snowstorm’ and ‘heatwave’ are mutually exclusive!
For more on this topic, check out our Probability Revision Videos
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Amy studied at the University of Bristol and is our revision blog guru. She only graduated recently so understands the pressures of being a student better than most, and is here to share her wisdom so that you revise effectively, smash your exams, succeed at school and write cracking university and job applications.