Symmetrical Distribution and Quartiles

A symmetrical distribution is one in which the data is evenly distributed on both sides of the mean. This means that the left and right halves of the distribution are mirror images of each other. When the distribution is symmetrical, the median, mean, and mode are all the same value.

Quartiles refer to the three points that divide a dataset into four equal parts. The first quartile (Q1) is the 25th percentile, the second quartile (Q2) is the median, and the third quartile (Q3) is the 75th percentile.

Halving the Sum of Q1 and Q3

When the sum of Q1 and Q3 is halved, the resulting value is the median (Q2) of the dataset. This is because the median is the midpoint of the distribution, and halving the sum of Q1 and Q3 gives us the midpoint.

In other words, if we have a dataset with a symmetrical distribution and we know the values of Q1 and Q3, we can calculate the median by halving the sum of Q1 and Q3.

Example

Let's say we have a dataset with a symmetrical distribution and the values of Q1 and Q3 are 10 and 20, respectively. To find the median, we can follow these steps:

1. Add Q1 and Q3: 10 + 20 = 30
2. Halve the sum: 30 / 2 = 15
3. The resulting value (15) is the median of the dataset.

Conclusion

In a symmetrical distribution, when the sum of Q1 and Q3 is halved, the resulting value is the median of the dataset. This is because the median is the midpoint of the distribution, and halving the sum of Q1 and Q3 gives us the midpoint. Therefore, the correct answer to the given question is option C – Median.

 The average of 1st and 3rd quartiles is 2nd quartile .