Compute mean, median and mode for the following data : 16, 17, 16, 16, 18, 19, 20, 36, 41, 17, 15, 16, 19, 11, 10, 5, 6, 7, 8, 20

Mean Calculation

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

For the given data set:
[ \text{Sum of values} = 16 + 17 + 16 + 16 + 18 + 19 + 20 + 36 + 41 + 17 + 15 + 16 + 19 + 11 + 10 + 5 + 6 + 7 + 8 + 20 = 310 ]
[ \text{Number of values} = 20 ]

[ \text{Mean} = \frac{310}{20} = 15.5 ]

So, the mean of the given data set is ( 15.5 ).

Median Calculation

The median is the middle value in a sorted data set. If the number of values in the data set is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.

First, let's sort the data set in ascending order:

[ 5, 6, 7, 8, 10, 11, 15, 16, 16, 16, 17, 17, 18, 19, 19, 20, 20, 36, 41 ]

Since the number of values is even (20), the median will be the average of the 10th and 11th values:

[ \text{Median} = \frac{16 + 17}{2} = \frac{33}{2} = 16.5 ]

So, the median of the given data set is ( 16.5 ).

Mode Calculation

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

From the sorted data set:
[ \text{Mode} = 16 ]

So, the mode of the given data set is ( 16 ).

Conclusion

In summary, for the given data set, the mean is 15.5, the median is 16.5, and the mode is 16. These measures provide different insights into the central tendency of the data. The mean represents the average value, the median represents the middle value, and the mode represents the most frequent value. These measures help summarize and understand the distribution of values in the data set.