You are given a dataset of 20 ages of participants in a science competition. The ages are as follows: 34, 29, 45, 42, 19, 38, 27, 23, 55, 34, 42, 51, 38, 29, 42, 45, 19, 56, 29, 34. Calculate the mean, median, and mode of the ages.

Sure, let's calculate the mean, median, and mode of the ages.

Step 1: Calculate the Mean The mean is the average of all numbers and is sometimes called the arithmetic mean. This can be calculated by adding all the numbers and then dividing by the quantity of numbers.

The sum of all ages is: 34 + 29 + 45 + 42 + 19 + 38 + 27 + 23 + 55 + 34 + 42 + 51 + 38 + 29 + 42 + 45 + 19 + 56 + 29 + 34 = 792

The total number of ages is 20.

So, the mean is 792 / 20 = 39.6

Step 2: Calculate the Median The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average.

First, let's sort the ages in ascending order: 19, 19, 23, 27, 29, 29, 29, 34, 34, 34, 38, 38, 42, 42, 42, 45, 45, 51, 55, 56

The total number of ages is 20, an even number, so the median is the average of the two middle numbers. In this case, the two middle numbers are the 10th and 11th numbers in the sorted list, which are both 34.

So, the median is (34 + 34) / 2 = 34

Step 3: Calculate the Mode The mode is the number that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all.

Looking at our sorted list of ages, we can see that the number 34, 29, 42 appears most frequently (3 times each).

So, the modes are 34, 29, and 42.

In conclusion, the mean age is 39.6, the median age is 34, and the modes are 34, 29, and 42.