Make up a data set of at least 12 numbers that have the following landmarks
Maximum 18
Mode 7
Range 13
Median 12
Make a bar graph of the data
we start knowing nothing:
x x x x x x x x x x x x
median=12 (average of 2 center values)
x x x x x 12 12 x x x x x
mode=7. we have 2 12's, so let's have 3 7's:
x x 7 7 7 12 12 x x x x x
max is 18:
x x 7 7 7 12 12 x x x x 18
range is 13, so min=5
5 x 7 7 7 12 12 x x x x 18
fill in the rest any way that fits:
5 6 7 7 7 12 12 13 14 15 16 17 18
oops. kill that 17 - too many values...
To create a dataset with the given landmarks, we need to find a set of numbers that satisfies the given conditions. Here is a possible dataset:
{1, 2, 3, 4, 6, 7, 7, 7, 10, 12, 14, 18}
Explanation:
- Maximum: The highest value in the dataset is 18.
- Mode: The mode is the value that appears most frequently. In this case, 7 appears three times, making it the mode.
- Range: The range is calculated by subtracting the smallest value from the largest value. In this case, 18 - 1 = 17, which is the range.
- Median: The median is the middle value in a dataset when it is sorted from least to greatest. In this case, when the dataset is sorted, the middle value is 12.
Now, let's create a bar graph to visualize this dataset. Each number will have its own bar, and the height of each bar will represent the frequency of that number in the dataset.
Bar graph:
Number - Bar height:
1 - ||
2 - |
3 - |
4 - |
6 - |
7 - |||
10 - |
12 - ||
14 - |
18 - ||
Note: The lengths of the bars are purely for illustration purposes and do not represent any specific value. The main focus is to represent the frequency of each number in the dataset.
To create a data set with the given landmarks, you can follow these steps:
1. Start by selecting a value for the mode, which is the most frequently occurring number. In this case, the mode is 7.
2. Determine the range, which is the difference between the maximum and minimum values. Here, the range is 13.
3. Choose a value for the median, which is the middle number when the data set is arranged in ascending order. In this case, the median is 12.
4. To achieve a maximum value of 18, select a number close to it that also adheres to the mode, range, and median conditions. A suitable choice could be 17.
5. With these values in mind, we can construct a data set containing at least 12 numbers. Here is an example:
7, 7, 7, 9, 11, 12, 12, 12, 12, 13, 16, 17
This data set satisfies the given landmarks of a maximum of 18, mode of 7, range of 13, and median of 12.
Now, let's create a bar graph to represent this data set:
1. On a piece of graph paper or using graphing software, draw a vertical axis labeled "Frequency" or "Count."
2. Draw a horizontal axis labeled "Values."
3. Along the horizontal axis, mark values from the lowest to the highest in your data set. In this case, you would mark from 7 to 17.
4. Above each value on the horizontal axis, draw vertical bars. The height of each bar represents the frequency or count of that value in the data set.
For example, the bar for the value 7 would have a height of 3 since it occurs three times in the data set.
Repeat this process for each value, adjusting the height of the bars according to their frequency.