Land area of US states
Stem-Leaf <---- This is a chart
0- 2,6,8,9
1- 1,3,4,4
2- 9
3- 8
key:1/3=130,000
Find the mode, median, mean, range, lower quartile range, upper quartile range, and interquartile range for data set. please help me
Don’t see your chart.
The key tells you what the numbers are.
1 | 3 is 130,000, which means the stem (1) holds the 100000's place and the leaf (3) holds the 10000's place.
So in your chart, the first piece of data is 0|2. Since 0 means there's nothing in the 100000's place, the number represented here is 20000. Another piece of data we see is 1|4, which means 140000. Note that this piece of data occurs twice in your chart. It's the only recurring one so it is the mode.
Count the leaves to see how many pieces of data you have...10. Since this is an even number, the median will be the average of the two middle pieces of data. Count leaves across rows from the top until you get to these middle leaves: the fifth and sixth leaves, 1 and 3. These are on the same row so we can average them directly to get 2. So the median is 1|2, or 120000.
Mean: [(sum of the stems × 100000) + (sum of the leaves × 10000)] / 10
Range: largest piece of data - smallest piece of data.
Lower quartile: middle of the first five pieces of data, so find that number in the chart.
Upper quartile: middle of the second five pieces of data.
Interquartile range: upper quartile - lower quartile.
To find the mode, median, mean, range, lower quartile range, upper quartile range, and interquartile range for a given dataset, follow these steps:
1. Mode: The mode is the value(s) that appear most frequently in the dataset. In this case, the mode is 2, as it appears the most times.
2. Median: The median is the middle value when the dataset is arranged in ascending order. To find the median, arrange the data values in numerical order:
0, 0, 0, 1, 1, 1, 1, 2, 3, 4, 4, 6, 8, 9, 9
Since there are 15 values, the middle value is the 8th value, which is 2. Therefore, the median is 2.
3. Mean: The mean is the average of all the values in the dataset. To find the mean, add up all the values and divide the sum by the total number of values:
(0 + 0 + 0 + 1 + 1 + 1 + 1 + 2 + 3 + 4 + 4 + 6 + 8 + 9 + 9) / 15
The sum is 49, so the mean is 49/15 ≈ 3.267.
4. Range: The range is the difference between the highest and lowest values in the dataset. In this case, the range is 9 - 0 = 9.
5. Lower Quartile Range: The lower quartile range is the difference between the median and the lowest value in the lower half of the dataset. To find it, first split the dataset into lower and upper halves. The lower half is 0, 0, 0, 1, 1, 1, 1, 2, and the median is 2. The difference is 2 - 0 = 2.
6. Upper Quartile Range: The upper quartile range is the difference between the highest value in the upper half of the dataset and the median. In this case, the upper half is 3, 4, 4, 6, 8, 9, 9, and the highest value is 9. The difference is 9 - 2 = 7.
7. Interquartile Range: The interquartile range is the difference between the upper quartile range and the lower quartile range. In this case, the interquartile range is 7 - 2 = 5.
So, the mode is 2, the median is 2, the mean is 3.267, the range is 9, the lower quartile range is 2, the upper quartile range is 7, and the interquartile range is 5.