what is the mean, median and mode also range of stem and leaf Plots?
Check these sites.
http://www.purplemath.com/modules/stemleaf.htm
http://www.purplemath.com/modules/meanmode.htm
To understand the mean, median, mode, and range of data represented in a stem and leaf plot, you need to follow these steps:
1. Constructing a stem and leaf plot:
- Sort the data in ascending order.
- Determine a stem, which consists of the leftmost digit(s) of each data point.
- Write down each data point's leaf, which is the rightmost digit, next to the corresponding stem.
Example: Let's take the data set {12, 15, 23, 28, 29, 30}.
Here, the stems would be 1, 1, 2, 2, 2, and 3, respectively, and the leaves would be 2, 5, 3, 8, 9, and 0, respectively. So the stem and leaf plot would look like this:
```
1 | 2 5
1 |
2 | 3 8 9
3 | 0
```
2. Computing the mean:
- Add up all the data points.
- Divide the sum by the total number of data points.
Example: The sum of our data set is 12 + 15 + 23 + 28 + 29 + 30 = 137. Since there are 6 data points, the mean would be 137 / 6 = 22.83 (rounded to two decimal places).
3. Calculating the median:
- Arrange the data points in ascending order.
- Find the middle value.
- If there are an odd number of data points, this value is the median.
- If there are an even number of data points, calculate the average of the two middle values.
Example: Since our data set has an even number of points, we arrange it in ascending order: 12, 15, 23, 28, 29, 30. The two middle values are 23 and 28, so the median would be (23 + 28) / 2 = 25.5.
4. Determining the mode:
- Identify the value(s) that appear most frequently in the data set.
Example: In our data set, no value appears more than once, so there is no mode.
5. Finding the range:
- Subtract the smallest data point from the largest data point.
Example: The smallest value in our data set is 12 and the largest value is 30. Therefore, the range would be 30 - 12 = 18.
So, for the given stem and leaf plot:
- Mean: 22.83 (rounded to two decimal places)
- Median: 25.5
- Mode: No mode exists
- Range: 18