Aaron is considering potential ways to allocate $50 he received for his birthday. Aaron has identified the following as potential options:
save to buy books for college
spend on an online SAT prep course
buy a new video game
What step of the rational decision-making model is Aaron on?
a
determining criteria
b
making a final decision
c
defining the problem
d
identifying alternatives
d - identifying alternatives
Hey bot Find the quartiles for the given dataset.
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
To find the quartiles, we need to first order the data set from smallest to largest:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
The second quartile (Q2) is simply the median of the dataset:
Q2 = 50
To find Q1 and Q3, we first need to find the median of the lower half and upper half of the dataset, respectively.
Lower half of the dataset:
35, 40, 40, 45, 45, 50
Upper half of the dataset:
55, 60, 60, 65, 70
Finding the median of the lower half:
Q1 = median of 35, 40, 40, 45, 45, 50
Q1 = (45 + 40)/2
Q1 = 42.5
Finding the median of the upper half:
Q3 = median of 55, 60, 60, 65, 70
Q3 = (60 + 65)/2
Q3 = 62.5
Therefore, the quartiles for the given dataset are as follows:
Q1 = 42.5
Q2 = 50
Q3 = 62.5
hey bot Find these measures of variability for the given dataset: range and IQR.
21, 24, 25, 27, 30, 32, 33, 34, 34, 36, 41
To find the range, we need to subtract the smallest value (21) from the largest value (41):
Range = 41 - 21 = 20
To find the interquartile range (IQR), we first need to find the quartiles.
Q1 = Median of the data below the median.
21, 24, 25, 27, 30, 32
Q1 = (25 + 27)/2
Q1 = 26
Q3 = Median of the data above the median.
34, 34, 36, 41
Q3 = (34 + 36)/2
Q3 = 35
Now we can calculate the IQR by subtracting Q1 from Q3:
IQR = 35 - 26 = 9
Therefore, the range of the given dataset is 20 and the IQR is 9.
hey bot For the given box plot, which measure of center—mean or median—best represents the shape of the distribution? Enter 1 for median or 2 for mean. (the numbers are 60,65,70,75,80,85,90,95,100)
Based solely on the box plot and without additional information about the data distribution, the median is the best measure of center to represent the shape of the distribution. This is because the median (represented by the line inside the box) divides the data into two halves, with 50% of the data below and 50% above. The box plot does not provide information about the data's symmetry or skewness, which are important when deciding which measure of center to use. Therefore, the answer is 1 for median.
hey bot Here are the blood pressure readings for Dr. Jackson’s patients yesterday. The systolic blood pressure numbers (top numbers) are given. Which measure of variability—MAD or IQR—best represents the shape of the distribution? Enter 1 for MAD or 2 for IQR.
70, 79, 82, 90, 96, 110, 120, 134, 139, 142, 148, 150, 152, 155, 161
To determine which measure of variability (MAD or IQR) best represents the shape of the distribution, we would need to first examine the shape of the distribution. However, without a visual representation or additional information about the distribution, it is difficult to determine which measure is more appropriate.
In general, the MAD is useful for distributions that are roughly symmetric or have a single peak (unimodal) and no significant outliers, while the IQR is more robust for distributions that may be skewed or have outliers.
Looking at the data, there appears to be a wide range of values, with some potentially high values towards the right end of the list. Therefore, the IQR may be more appropriate for this dataset to capture the variability in the middle 50% of the data while being resistant to outliers. Hence, the answer is 2 for IQR.
hey bot Summarize the dataset by finding its measures of center—mean, median, and mode.
20, 30, 32, 16, 31, 32, 13, 20, 28, 32, 15, 18, 20, 21, 32