The median is the central datum. To find it, first arrange the data in ascending order. If the data size is odd, the median is the centre value. That is, if there are n items then the value is at the (n+1)/2 position counting from either end of the dataset.
If the data size is even then the median is the average of the two central data values. The average is half the sum of the values.
The mode (if there is one) is the data value which is the most repeated value.
Stem and leaf plot is a way of getting the data into order, especially if there's a lot of data. The stem is some common part of the data values, which are believed to be easy to put into order. The leaves are the data values listed in order which have the same stem. The stems form a column while the leaves make up the rows for the stems. The plot is the appearance of the lengths of the rows compared with one another.
Since no data has been supplied with this question, there are some examples below.
EXAMPLES
Median
Dataset: 8, 45, 1, 6, 18, 12, 20⇒1, 6, 8, 12, 18, 20, 45; median is 12.
Dataset: 3, -1, 1, 0, 2, 4⇒-1, 0, 1, 2, 3, 4; median is 1.5.
In the above datasets there is no mode (no value is repeated).
13.4, 14.5, 12.0, 11.8, 14.5, 12.5, 13.0, 13.4, 14.5. No ordering is necessary to find the mode, but it can help to identify which value is most repetitive, because it brings the same data values together. In this case the mode is 14.5.
Stem and leaf plot
Dataset: 158, 162, 168, 155, 167, 154, 164, 159, 163, 151, 153, 163, 170, 164, 157.
Use the first two digits as the stem, so the stems are 15, 16 and 17:
15: 1, 3, 4, 5, 7, 8, 9
16: 2, 3, 3, 4, 4, 7, 8
17: 0
The single digit leaves are written in order alongside their 2-digit stems. The leaves form a shape in which the rows of the 15 and 16 stems have equal "length" in this example.
The more data there is and the identification of a suitable stem to provide a reasonable number of rows, the easier it is to see by the lengths of the rows what the spread of the data looks like.