Compute mean, median and mode for the following data : 16, 18, 19, 21, 16, 10, 11, 16, 17, 19, 21, 24, 15, 9, 8, 4, 3, 16, 18, 21.

1. Calculation of Mean

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

Mean = (Sum of all values) / (Total number of values)

For the given dataset:
Sum of all values = 16 + 18 + 19 + 21 + 16 + 10 + 11 + 16 + 17 + 19 + 21 + 24 + 15 + 9 + 8 + 4 + 3 + 16 + 18 + 21 = 317
Total number of values = 20

Mean = 317 / 20 = 15.85

Mean = 15.85

2. Calculation of Median

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

Step 1: Arrange the values in ascending order:
3, 4, 8, 9, 10, 11, 15, 16, 16, 16, 16, 17, 18, 18, 19, 19, 21, 21, 21, 24

Step 2: Identify the middle value(s):
Since there are 20 values in the dataset, the median is the average of the 10th and 11th values.
Median = (16 + 16) / 2 = 16

Median = 16

3. Calculation of Mode

The mode is the value that occurs most frequently in the dataset.

For the given dataset, the frequency of each value is as follows:
3: 1, 4: 1, 8: 1, 9: 1, 10: 1, 11: 1, 15: 1, 16: 4, 17: 1, 18: 2, 19: 2, 21: 3, 24: 1

The value 16 occurs most frequently in the dataset, with a frequency of 4.

Mode = 16

Conclusion

In summary, for the given dataset:

• Mean = 15.85
• Median = 16
• Mode = 16

These measures of central tendency provide insights into the typical or central value of the dataset. The mean represents the average value, the median represents the middle value, and the mode represents the most frequently occurring value.