Compute mean, median and mode for the following data : 14, 17, 19, 19, 20, 19, 17, 18, 15, 19, 19, 13, 12, 9, 8.

1. Mean

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

To compute the mean for the given dataset:

Mean = (14 + 17 + 19 + 19 + 20 + 19 + 17 + 18 + 15 + 19 + 19 + 13 + 12 + 9 + 8) / 15

Mean = 262 / 15

Mean ≈ 17.47

Therefore, the mean of the given dataset is approximately 17.47.

2. Median

The median is the middle value of a dataset when it is 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.

To compute the median for the given dataset:

1. Arrange the dataset in ascending order:
   8, 9, 12, 13, 14, 15, 17, 17, 18, 19, 19, 19, 19, 20

2. Since there are 15 values, the median is the 8th value in the ordered list:
   Median = 17

Therefore, the median of the given dataset is 17.

3. Mode

The mode is the value that appears most frequently in the dataset. A dataset may have one mode (unimodal), two modes (bimodal), or more than two modes (multimodal).

To compute the mode for the given dataset:

1. Count the frequency of each value:
2. 8 appears once
3. 9 appears once
4. 12 appears once
5. 13 appears once
6. 14 appears once
7. 15 appears once
8. 17 appears twice
9. 18 appears once
10. 19 appears four times

11. 20 appears once

12. The value with the highest frequency is the mode:
    Mode = 19

Therefore, the mode of the given dataset is 19.

Conclusion

In summary, for the given dataset:

• Mean ≈ 17.47
• Median = 17
• Mode = 19

These measures of central tendency provide insights into the typical or central value of the dataset, helping to summarize and interpret the data effectively.