The correct answer is option 'D' - median.

The median is a measure of central tendency that represents the middle value in a dataset when the data is arranged in order of magnitude. It is the value that divides the dataset into two equal halves, with an equal number of data points on either side.

To understand why the median represents the middlemost item when arranged in order of magnitude, let's consider an example. Suppose we have a dataset of 7 numbers: 2, 5, 6, 8, 10, 12, 15.

- Arrange the data in order of magnitude: 2, 5, 6, 8, 10, 12, 15.
- The middle value is the fourth number, which is 8.

In this example, the median is 8 because it is the middlemost value when the data is arranged in order of magnitude. It is important to note that the median is not affected by extreme values or outliers, unlike the mean.

The mean (option 'B') is another measure of central tendency that represents the average value of a dataset. It is calculated by summing up all the values in the dataset and dividing it by the total number of values. However, the mean does not necessarily represent the middlemost item when arranged in order of magnitude.

The mode (option 'C') is the value that appears most frequently in a dataset. It is not related to the middlemost item when arranged in order of magnitude.

The standard deviation (option 'A') is a measure of dispersion or spread in a dataset. It quantifies how much the values in a dataset deviate from the mean. It is not related to the middlemost item when arranged in order of magnitude.

In summary, the middlemost item when arranged in order of magnitude is called the median. It is a measure of central tendency that represents the middle value in a dataset.