Mrs. Rodriguez randomly surveyed 15 of her ninth grade students on how many hours they spent completing assignments and preparing for assessments last week:
0.5 0.5 1.0 1.5 1.5 1.5 2 2 2.5 3 3 3.5 5 8 10
Which measure of variability—range or IQR—best describes the spread of the dataset? Enter 1 for range or 2 for IQR.
(1 point)
UHM BOT THAT IS WRONG
2
To determine which measure of variability best describes the spread of the dataset, we need to calculate both the range and the IQR (Interquartile Range) and compare them.
The range is calculated by subtracting the smallest value from the largest value. In this case:
Range = 10 - 0.5 = 9.5
The IQR is the difference between the upper quartile (Q3) and the lower quartile (Q1). To calculate the IQR, we first need to find the quartiles.
To find the quartiles, we need to sort the dataset in ascending order:
0.5, 0.5, 1.0, 1.5, 1.5, 1.5, 2, 2, 2.5, 3, 3, 3.5, 5, 8, 10
There are 15 data points in the dataset, so the median will be the 8th value. Since there are two values in the middle, we take the average of the 8th and 9th values:
Median = (2 + 2.5) / 2 = 2.25
To find Q1, we consider the values below the median. Since there are 7 values below the median, the median of these values will be the 4th value:
Q1 = 1.5
To find Q3, we consider the values above the median. Since there are 7 values above the median, the median of these values will be the 12th value:
Q3 = 3.5
Now we can calculate the IQR:
IQR = Q3 - Q1 = 3.5 - 1.5 = 2
Comparing the range (9.5) and the IQR (2), it is clear that the IQR is a better measure of variability for this dataset.
Therefore, the answer is 2 for IQR.
To determine which measure of variability best describes the spread of the dataset, we need to calculate both the range and the interquartile range (IQR) and compare them.
1. Range:
The range is the difference between the maximum and minimum values in the dataset.
The maximum value is 10, and the minimum value is 0.5.
Range = Maximum - Minimum = 10 - 0.5 = 9.5
2. IQR:
The interquartile range is a measure of spread that eliminates outliers and is less influenced by extreme values. To calculate the IQR, we need to find the first quartile (Q1) and third quartile (Q3).
To find Q1:
- Sort the dataset in ascending order: 0.5, 0.5, 1.0, 1.5, 1.5, 1.5, 2, 2, 2.5, 3, 3, 3.5, 5, 8, 10.
- Since we have 15 data points, Q1 will be the value at the 25th percentile.
- (25 / 100) * 15 = 3.75, which is between the 3rd and 4th value in the dataset.
- Q1 = (1.5 + 1.5) / 2 = 1.5
To find Q3:
- Q3 will be the value at the 75th percentile.
- (75 / 100) * 15 = 11.25, which is between the 11th and 12th value in the dataset.
- Q3 = (3 + 3.5) / 2 = 3.25
IQR = Q3 - Q1 = 3.25 - 1.5 = 1.75
Now, to determine which measure of variability best describes the spread of the dataset, we compare the range and the IQR.
If the range is relatively high compared to the IQR, it means there are extreme values or outliers in the dataset. In this case, the IQR would be a better measure of variability because it is less influenced by outliers.
However, if the range is relatively small compared to the IQR, it means the values are relatively evenly spread out without extreme outliers. In this case, the range would be a better measure of variability.
Comparing the values we calculated:
- Range = 9.5
- IQR = 1.75
The range (9.5) is much larger compared to the IQR (1.75), indicating the presence of outliers. Therefore, the best measure of variability to describe the spread of the dataset is the range.
So the answer is: 1 for range.