Question

i. the means of the classes differ by less than one point.
ii. class 2 has a greater median compared to class 1.
iii. class 1 has a greater interquartile range compared to class 2.
iv. class 2 has a greater standard deviation than class 1.
a. i and ii
b. ii and iii
c. ii and iv
d. i and iv

Explanation:

Step1: Analyze the median

• For class 1, the data is more spread out towards lower values. For class 2, the data is more spread out towards higher values. By visual inspection (since the median is the middle - value when data is ordered), class 2 has a greater median.

Step2: Analyze the standard deviation

• Standard deviation measures the spread of data. Class 1 has data more clustered (less spread out), while class 2 has data more spread out. So class 2 has a greater standard deviation.

Step3: Analyze the mean

• To calculate the mean precisely would require assigning values to each dot (which is time - consuming here). But by visual inspection, the means do not differ by less than one point. Class 1 has more data on the lower end (pulling its mean down) and class 2 has more data on the higher end (pulling its mean up), and the difference is more than one.

Step4: Analyze the inter - quartile range

• The inter - quartile range (IQR) is \(Q3 - Q1\). Class 1 has data more clustered, so its IQR is less than that of class 2 (since class 2 has more spread out data).

Answer:

C. II and IV