Question

the dot - plots represent the cost of first - year college tuitions for two different u.s regions. which of the statements are true? cost of first - year tuition in region 1 number of universities cost of tuition (us dollars in thousands) cost of first - year tuition in region 2 number of universities cost of tuition (us dollars in thousands) i. region 1 has a greater mean than region 2. ii. region 2 has a greater median than region 1. iii. region 1 has a greater interquartile range than region 2. iv. region 2 has a greater standard deviation than region 1. a. iii and iv b. i and iii c. ii and iv d. i and ii

Explanation:

Step1: Analyze the mean

Visually, the data - points in Region 1 are more spread out towards the higher - cost values compared to Region 2. The mean is the sum of all values divided by the number of values. Since the higher - cost values in Region 1 pull the mean upwards, Region 1 has a greater mean.

Step2: Analyze the median

The median is the middle value when the data is arranged in ascending order. Region 2 has more data - points concentrated towards the middle values, and visually, the middle value (median) of Region 2 is greater than that of Region 1.

Step3: Analyze the inter - quartile range (IQR)

The IQR is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$). Visually, the spread of the middle 50% of the data (IQR) in Region 1 is greater than in Region 2.

Step4: Analyze the standard deviation

The standard deviation measures the amount of variation or dispersion of a set of values. Region 2 has data more concentrated around the middle values compared to Region 1, so Region 1 has a greater standard deviation.

Answer:

B. I and III