Calculate mean, median, and mode for grouped data, using direct, assumed mean, and step-deviation methods.
The direct method uses Σfx/Σf. The assumed mean and step-deviation methods simplify calculations using deviations from a chosen value.
Class marks 10,20,30 with frequencies 2,3,5. Find the mean.
(10×2+20×3+30×5)/(2+3+5)=(20+60+150)/10=230/10=23
Why is the step-deviation method preferred for large class widths?
It divides deviations by the class width, keeping numbers small and calculations manageable
Class marks 20,30,40 with frequencies 5,7,3. Find the mean.
(20×5+30×7+40×3)/(5+7+3)=(100+210+120)/15≈28.67
Median uses the cumulative frequency to locate the median class, then interpolates. Mode uses the modal class's frequencies in a specific formula.
A data set has 60 observations. What cumulative frequency value locates the median class?
n/2=30
What determines the modal class?
The class interval with the highest frequency
A data set has 70 observations. What cumulative frequency locates the median class?
n/2=35
1. Class marks 15,25,35 with frequencies 4,6,2. Find the mean.
2. A data set has 80 observations. What cumulative frequency locates the median class?
3. What class is called the modal class in a frequency distribution?
4. Class marks 5,15,25 with frequencies 3,5,2. Find the mean.
5. Why might mean, median, and mode all differ for a skewed data set?
6. Class marks 10,20,30 with frequencies 6,4,2. Find the mean.
7. A data set has 100 observations. What cumulative frequency locates the median class?
8. What class is called the modal class?
9. Class marks 25,35,45 with frequencies 8,5,7. Find the mean.
10. Why might mean and median differ significantly for skewed data?