Compute mean, median and mode for the following data : 21, 31, 42, 43, 44, 46, 47, 51, 43, 44, 47, 44, 44, 45, 44, 49, 50, 51, 52, 56, 71, 82, 83, 84, 85.

1. Introduction

In this task, we will compute the mean, median, and mode for the given dataset.

2. Mean Calculation

The mean, also known as the average, is calculated by summing up all the values in the dataset and dividing by the total number of values.

Mean = (21 + 31 + 42 + 43 + 44 + 46 + 47 + 51 + 43 + 44 + 47 + 44 + 44 + 45 + 44 + 49 + 50 + 51 + 52 + 56 + 71 + 82 + 83 + 84 + 85) / 25

Mean = 1347 / 25

Mean = 53.88

Therefore, the mean of the given dataset is approximately 53.88.

3. Median Calculation

The median is the middle value in a dataset when the values are arranged in ascending or descending order. If there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.

First, let's arrange the data in ascending order:

21, 31, 42, 43, 43, 44, 44, 44, 44, 44, 45, 46, 47, 47, 49, 50, 51, 51, 52, 56, 71, 82, 83, 84, 85

As there are 25 values, the median will be the 13th value, which is 46.

Therefore, the median of the given dataset is 46.

4. Mode Calculation

The mode is the value that appears most frequently in a dataset. A dataset may have one mode, more than one mode (multimodal), or no mode if all values occur with the same frequency.

In the given dataset, the value 44 appears most frequently, occurring 5 times. Therefore, the mode of the dataset is 44.

5. Summary

• Mean: 53.88
• Median: 46
• Mode: 44

6. Conclusion

In conclusion, the mean, median, and mode of the given dataset have been calculated. These measures provide different insights into the central tendency of the dataset, with the mean representing the average value, the median representing the middle value, and the mode representing the most frequently occurring value. These measures are useful for summarizing and understanding the distribution of numerical data.