Compute mean, median and mode for the following data : 12, 12, 13, 16, 12, 15, 19, 10, 11, 9, 7, 6, 5, 10, 4.

Mean, Median, and Mode Calculation

1. Mean:
The mean, also known as the average, is calculated by summing up all the values in the data set and then dividing the sum by the total number of values.

Mean = (12 + 12 + 13 + 16 + 12 + 15 + 19 + 10 + 11 + 9 + 7 + 6 + 5 + 10 + 4) / 15

Mean = 175 / 15

Mean = 11.67

2. Median:
The median is the middle value of the data set when the values are arranged in ascending or descending order. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values.

First, let's arrange the data set in ascending order:
4, 5, 6, 7, 9, 10, 10, 11, 12, 12, 12, 13, 15, 16, 19

Since the data set has an odd number of values (15), the median is the middle value, which is the 8th value: 11.

3. Mode:
The mode is the value that appears most frequently in the data set.

In this data set, the value 12 appears most frequently, occurring three times. Therefore, the mode is 12.

Conclusion:
In summary, for the given data set:

• Mean = 11.67
• Median = 11
• Mode = 12

These measures provide different perspectives on the central tendency of the data. The mean gives us the average value, the median gives us the middle value, and the mode gives us the most frequently occurring value. Each measure has its strengths and limitations, and using all three can provide a more comprehensive understanding of the data's distribution and central tendency.