Central tendency & spread
Practice Flashcards
How do you find the mean of a list?
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All Flashcards in Topic 4.3
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4.3.19 cards
How do you find the mean of a list?
Add all the values and divide by how many there are (Σx ÷ n).
What is the median?
The middle value when the data is put in order.
What is the mode?
The value that occurs most often.
How do you find the mean from a frequency table?
Σfx ÷ Σf — multiply each value by its frequency, add, then divide by the total frequency.
What do you divide by for the mean of a frequency table?
The total frequency Σf, not the number of different values.
If the mean of n values is known, how do you get the total?
Total = mean × n.
Which average is least affected by outliers?
The median.
Which average is pulled toward extreme values?
The mean.
When is the mode the only usable average?
For categorical (non-numeric) data, where you can't add or order values.
4.3.29 cards
How do you estimate the mean of grouped data?
Use Σfx ÷ Σf with x = the class midpoints.
How do you find a class midpoint?
(lower boundary + upper boundary) ÷ 2.
Why is the grouped-data mean only an estimate?
The exact values within each class are unknown, so midpoints are used to represent them.
What is the modal class?
The class with the greatest frequency.
What is the median class?
The class containing the (n/2)-th value, found from the running (cumulative) total.
Are the modal class and median class always the same?
No — they are often different classes; find each separately.
How do you find a missing frequency from a given mean?
Set Σfx ÷ Σf = the given mean (x = midpoints) and solve for the unknown frequency.
What goes in the denominator of the estimated mean?
Σf, the total frequency.
On Paper 2, how do you get the grouped mean quickly?
Enter the midpoints as the data list and the frequencies as the frequency list, then run 1-Var Stats.
4.3.39 cards
How do you find the median of an ordered list?
It is the middle value (for odd n) or the mean of the two middle values (for even n).
What is the lower quartile Q1?
The median of the lower half of the ordered data.
What is the upper quartile Q3?
The median of the upper half of the ordered data.
For odd n, do you include the median in the halves?
No — leave the median out of both halves before finding the quartiles.
What is the range?
Maximum − minimum.
What is the interquartile range?
IQR = Q3 − Q1, the spread of the middle 50%.
Why is the IQR preferred to the range when there are outliers?
The IQR uses only the quartiles, so extreme values barely change it.
For an even number of values, what is the median?
The mean of the two middle values.
On Paper 2, how do you get the quartiles quickly?
Enter the data in a list and run 1-Var Stats — it lists Q1, Med and Q3.
4.3.49 cards
What does the standard deviation measure?
How far values typically lie from the mean — the spread of the data.
What does a small standard deviation tell you?
The data is clustered close to the mean.
What is the variance?
The standard deviation squared (σ²).
How do you find the standard deviation on Paper 2?
Enter the data in a list and run 1-Var Stats; read σx.
Which output is the standard deviation: σx or Sx?
σx — the population standard deviation used in the IB syllabus.
How do you enter a frequency table for 1-Var Stats?
Values in one list, frequencies in another, then run 1-Var Stats with both lists.
If you add c to every value, what happens to the mean and σ?
The mean increases by c; the standard deviation is unchanged.
If you multiply every value by k, what happens to the mean and σ?
Both are multiplied by |k|.
How do you get σ from the variance?
Take the square root: σ = √variance.
Topic 4.3 study notes
Full notes & explanations for Central tendency & spread
Math AA SL exam skills
Paper structures, command terms & tips
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