Calculate mean, median, and mode for grouped data using direct, assumed mean, and step-deviation methods.
The direct method sums fx/f. The assumed mean method and step-deviation method simplify calculation for large data sets by working with deviations from an assumed mean.
Data: class marks 10,20,30 with frequencies 3,5,2. Find the mean using the direct method.
Mean=(10×3+20×5+30×2)/(3+5+2)=(30+100+60)/10=190/10=19
Why use the step-deviation method for large data values?
It simplifies arithmetic by dividing deviations by the class width, reducing the size of numbers used in calculation
For grouped data, median uses the formula involving the cumulative frequency of the median class, and mode uses the formula based on the modal class's frequencies.
What class is called the 'median class' in grouped data?
The class interval where the cumulative frequency first reaches or exceeds n/2
What class is called the 'modal class'?
The class interval with the highest frequency
1. Data: class marks 5,15,25 with frequencies 4,6,2. Find the mean using the direct method.
2. A data set has 50 total observations. Find n/2, used to identify the median class.
3. What determines the 'modal class' in a frequency distribution?
4. Data: class marks 12,22,32 with frequencies 5,8,7. Find the mean.
5. Why might the mean, median, and mode differ for the same data set?