37 exam-style questions on Central tendency and dispersion; grouped data; quartiles — topic 4.3 of Statistics and Probability in the IB Mathematics: Applications and Interpretation syllabus — with answers and explanations. Samples below; the full set is free with an account.
A grouped frequency table has classes with mid-interval values 5, 15, 25 and frequencies 4, 10, 6. Calculate an estimate of the mean.
Answer: 16
Estimated mean = Σ(fx)/Σf = (5×4 + 15×10 + 25×6)/(4+10+6) = (20 + 150 + 150)/20 = 320/20 = 16.
A data set has 30 values. When ordered, determine the positions used to find the median.
Answer: The mean of the 15th and 16th values
For n = 30 (even), the median is the average of the values at positions n/2 = 15 and n/2 + 1 = 16.
The data set 6, 9, 9, 10, 12, 15, 18, 21 has 8 values. Determine the lower quartile Q1 using the position (n+1)/4.
Answer: 9
Q1 position = (8 + 1)/4 = 2.25, which lies between the 2nd and 3rd values; both are 9, so Q1 = 9. The GDC method (median of the lower half 6, 9, 9, 10) also gives 9.
A data set has mean 50 and standard deviation 8. Every value is multiplied by 3. Determine the new mean and new standard deviation.
Answer: Mean 150, standard deviation 24
Multiplying every value by 3 multiplies both the mean and the standard deviation by 3: mean = 150, standard deviation = 24.
A small company reports employee salaries where most staff earn near the median but one director earns far more. State which measure of central tendency is most affected by that director's salary.
Answer: The mean
The mean uses every value and is pulled upward by extreme high values, whereas the median and mode are resistant to such outliers.
For the data set 2, 4, 4, 5, 5, 5, 7, 8 (8 values), determine the interquartile range using Q1 = mean of the 2nd and 3rd values and Q3 = mean of the 6th and 7th values.
Answer: 2
Q1 = (4 + 4)/2 = 4 and Q3 = (5 + 7)/2 = 6, so IQR = 6 − 4 = 2.
That was 6 of 37 Central tendency and dispersion; grouped data; quartiles questions.
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37 Central tendency and dispersion; grouped data; quartiles questions — free with an account. Spaced repetition, streaks and full exam simulations included.
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