you create the data create a set of seven numbers (repeats allowed) that have the five numbers summary. minimum =4 Q1=8 M=12 Q3=15 Maximum=19.
There is more than one set of seven numbers with this five number summary. What must be true about the seven numbers to have this five number summary
To create a set of seven numbers that have the given five-number summary (minimum = 4, Q1 = 8, median = 12, Q3 = 15, maximum = 19), the numbers must satisfy the following conditions:
1. The minimum value must be at least 4.
2. The first quartile (Q1) value must be at least 8.
3. The median (M) value must be 12.
4. The third quartile (Q3) value must be at least 15.
5. The maximum value must be 19 or less.
As for the other two numbers in the set, they can vary as long as they meet the above conditions. There are many possible combinations that could satisfy these conditions. Here is one example of a set of seven numbers that meet the criteria:
4, 8, 10, 12, 15, 16, 19
In this set, the minimum is 4, Q1 is 8, median is 12, Q3 is 15, and the maximum is 19.
To determine the seven numbers that have the given five number summary (minimum, Q1, median, Q3, and maximum), you need to understand the statistical concepts and calculations involved.
1. The minimum value is given as 4, which means the lowest value in the dataset is 4.
2. The first quartile (Q1) is given as 8, which represents the 25th percentile of the dataset. This means that 25% of the data falls below 8.
3. The median (M) is given as 12, which represents the middle value of the dataset when it is sorted in ascending order.
4. The third quartile (Q3) is given as 15, which represents the 75th percentile of the dataset. This means that 75% of the data falls below 15.
5. The maximum value is given as 19, which means the highest value in the dataset is 19.
To have this particular five number summary, the seven numbers must satisfy the following conditions:
- There must be at least four numbers less than or equal to 8 (Q1) and at least three numbers greater than or equal to 15 (Q3), ensuring that the lower quartile and upper quartile are met.
- The median (12) must be located between 25% and 75% of the data, ensuring that it divides the dataset into two equal halves.
- The dataset should have a range of 19-4 = 15, which covers the distance between the minimum and maximum values.
Here is one example of a set of seven numbers that satisfies these conditions:
4, 4, 6, 8, 12, 15, 19
Note that there can be multiple sets of seven numbers that meet the given five number summary, as long as they meet the conditions outlined above.
To start with, any 7-number set with the given 5 number summary will look like this:
4, _, _, _, _, _, 19
Since there's an odd number of pieces of data, the middle value is the median, M, so the set must also look like this:
4, _, _, 12, _, _, 19
Now think about how lower quartile and upper quartile are calculated, to see what else must be true about the 7-number set.