Question

1. the box plots show the math test scores of students that took the test in the afternoon (top) versus those who took the test in the morning (bottom).

which class has a higher iqr? afternoon
which class has a higher average? morning

1. the following data shows the weights of housecats and small dogs. write true or false for each statement. if it is false, correct the statement.

weights (lb)
5 6 7 8 9 10 11 12 13 14
housecats
5 6 7 8 9 10 11 12 13 14
small dogs

a. housecats have a higher standard deviation. false
b. small dogs have more variability than housecats. true
c. the median of housecats is equal to the median of small dogs. true
d. the median of housecats is larger than the median of small dogs.
e. the mean and median of small dogs are equal. false
f. small dogs typically weigh more than housecats. false

Explanation:

Step1: Recall IQR concept

IQR = Q3 - Q1. For box - plots, we can visually estimate Q1 and Q3. For the afternoon class, assume Q1 is around 70 and Q3 is around 85, so IQR_aft = 85 - 70=15. For the morning class, assume Q1 is around 75 and Q3 is around 80, so IQR_mor = 80 - 75 = 5. So the afternoon class has a higher IQR.

Step2: Analyze mean from box - plot

The position of the median line and the overall spread in the box - plot can give an idea of the mean. The median of the morning class is higher and the distribution seems more concentrated around higher values compared to the afternoon class, so the morning class has a higher average.

Step3: Analyze standard deviation from dot - plot

Standard deviation measures the spread of data. The data points for small dogs are more spread out than for housecats, so housecats do not have a higher standard deviation (False). Small dogs have more variability (True).

Step4: Find medians

For housecats, arranging the data points in order, the median is 10. For small dogs, arranging the data points in order, the median is 10. So the median of housecats is equal to the median of small dogs (True).

Step5: Check mean - median equality for small dogs

The data for small dogs is not symmetric, so the mean and median are not equal (False).

Step6: Compare typical weights

Since the median and overall distribution of housecats' weights is not lower than that of small dogs, small dogs do not typically weigh more than housecats (False).

Answer:

a. Afternoon
b. Morning
c. False
d. True
e. True
f. False
g. False