Which measures of center does not change when a value of 0 is inserted into these datasets?
Dataset 1:
(12,19,18,12,19,14,12,28,22,10)
Dataset 2:
(12,19,18,12,19,14,12,28,22,10,0)
The median and the mode do not change when a value of 0 is inserted into both datasets.
The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. What are the first and third quartiles?
To find the first and third quartiles, we need to divide the set of prime numbers into four equal parts.
The first quartile (Q1) represents the value below which 25% of the data falls. Since there are 10 prime numbers in total, the first quartile corresponds to the value in the 2.5th position. However, this position does not exist within the list of prime numbers, as it is between the second and third prime numbers. Therefore, we take the average of the values in the second and third positions to calculate Q1.
Q1 = (3 + 5) / 2 = 4
The third quartile (Q3) represents the value below which 75% of the data falls. The 75th percentile in this case falls between the 7th and 8th prime numbers. Thus, we take the average of 17 and 19 to find Q3.
Q3 = (17 + 19) / 2 = 18
Therefore, the first quartile (Q1) is 4 and the third quartile (Q3) is 18.
What is the median of the box plot
To determine the median of the box plot, we need to find the median of the given set of prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Since the set has an even number of values (10), the median is the average of the two middle values. In this case, the two middle values are the 5th and 6th numbers in the set, which are 11 and 13.
Median = (11 + 13) / 2 = 24 / 2 = 12
Therefore, the median of the box plot is 12.
To identify which measures of center do not change when a value of 0 is inserted into the datasets, we need to calculate the measures of center for each dataset before and after the insertion of 0.
Dataset 1:
Before insertion of 0:
- Mean: 15.6
- Median: 14
After insertion of 0:
- Mean: (12+19+18+12+19+14+12+28+22+10+0)/11 = 14.54
- Median: 14
In Dataset 1, the median remains the same after inserting 0, but the mean changes.
Dataset 2:
Before insertion of 0:
- Mean: 15.6
- Median: 14
After insertion of 0:
- Mean: (12+19+18+12+19+14+12+28+22+10+0+0)/12 = 13.83
- Median: 13.5
In Dataset 2, both the mean and median change after inserting 0.
Therefore, in Dataset 1, the median does not change when a value of 0 is inserted, while in Dataset 2, neither the mean nor the median remain the same.
To identify the measure of center that does not change when a value of 0 is inserted into the datasets, we can calculate the mean and median for both datasets and see which ones remain the same.
Dataset 1: (12, 19, 18, 12, 19, 14, 12, 28, 22, 10)
Mean (Average):
To find the mean, add up all the values in the dataset and divide the sum by the number of values.
Sum = 12 + 19 + 18 + 12 + 19 + 14 + 12 + 28 + 22 + 10 = 166
Number of values = 10
Mean = 166 / 10 = 16.6
Median:
To find the median, arrange the numbers in ascending order and find the middle value.
Sorted dataset: (10, 12, 12, 12, 14, 18, 19, 19, 22, 28)
Middle value = 14
Therefore, in Dataset 1, the mean is 16.6 and the median is 14.
Dataset 2: (12, 19, 18, 12, 19, 14, 12, 28, 22, 10, 0)
Mean (Average):
Sum = 12 + 19 + 18 + 12 + 19 + 14 + 12 + 28 + 22 + 10 + 0 = 166
Number of values = 11
Mean = 166 / 11 = 15.09 (rounded to two decimal places)
Median:
Sorted dataset: (0, 10, 12, 12, 12, 14, 18, 19, 19, 22, 28)
Middle value = 14
Therefore, in Dataset 2, the mean is 15.09 and the median is 14.
Comparing the results, we can see that the median remains the same when a value of 0 is inserted into both datasets, while the mean changes. Therefore, the measure of center that does not change when a value of 0 is inserted into the datasets is the median.