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
The mean is calculated by adding up all of the values and dividing by the total number of values.
mean = (20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32) / 15 = 24.8
The median is the middle value when the data set is ordered from smallest to largest.
In order: 13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32
median = 24
The mode is the value that occurs most frequently in the data set.
mode = 32 (which occurs three times)
Therefore, the measures of center for the given dataset are as follows:
Mean = 24.8
Median = 24
Mode = 32
hey bot What are the quartiles for the given dataset?
115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
To find the quartiles, we first need to order the dataset from smallest to largest:
115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
Next, we can find the median, which is the second quartile (Q2):
Q2 = Median of the dataset = (125 + 127)/2 = 126
To find the value of Q1 (the first quartile), we need to find the median of the lower half of the dataset, which consists of the values below Q2 (126):
115, 117, 120, 122, 125, 125
Q1 = Median of the lower half of the dataset = (120 + 122)/2 = 121
To find the value of Q3 (the third quartile), we need to find the median of the upper half of the dataset, which consists of the values above Q2 (126):
128, 131, 132, 136, 136, 140
Q3 = Median of the upper half of the dataset = (132 + 136)/2 = 134
Therefore, the quartiles for the given dataset are:
Q1 = 121
Q2 = 126
Q3 = 134
Hey bot What is the MAD and IQR for the given dataset?
1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19
To find the MAD (median absolute deviation), we need to find the median of the absolute deviations of each data point from the median of the dataset.
First, we can find the median of the dataset:
Median = (11 + 12) / 2 = 11.5
Next, we can calculate the absolute deviation of each data point from the median:
|-10.5|, |-7.5|, |-5.5|, |-4.5|, |-2.5|, |-1.5|, |-1.5|, |-0.5|, |0.5|, |0.5|, |2.5|, |3.5|, |5.5|, |6.5|, |7.5|
The median of these absolute deviations is the MAD:
MAD = (2.5 + 2.5) / 2 = 2.5
To find the IQR (interquartile range), we can use the quartiles we calculated earlier:
Q1 = 6.5
Q3 = 16.5
IQR = Q3 - Q1 = 10
Therefore, the MAD and IQR for the given dataset are:
MAD = 2.5
IQR = 10