Question

a. what quarter has the smallest spread of data? fourth third second first b. what is that spread? c. what quarter has the largest spread of data? third first second fourth d. what is that spread? e. find the inter - quartile range (iqr): f. which interval has the most data in it? 43 - 57 75 - 100 57 - 61 67 - 74

Explanation:

Step1: Recall quartile spread concept

The spread of a quartile is the difference between the upper and lower values of that quartile. For a box - and - whisker plot, the first quartile (Q1) is at 57, the second quartile (Q2, median) has lower value 58 and upper value 61, the third quartile (Q3) is at 67 and the fourth quartile has lower value 67 and upper value 74.

Step2: Calculate spreads for each quartile

First quartile spread: Since it's from the minimum (43) to Q1 (57), we assume the spread is 57 - 43=14. Second quartile spread: 61 - 58 = 3. Third quartile spread: 67 - 61=6. Fourth quartile spread: 74 - 67 = 7.

Step3: Answer part a

The second quartile has the smallest spread of data.

Step4: Answer part b

The spread of the second quartile is 3.

Step5: Answer part c

The first quartile has the largest spread of data.

Step6: Answer part d

The spread of the first quartile is 14.

Step7: Calculate the inter - quartile range (IQR)

IQR=Q3 - Q1. Here, Q3 = 67 and Q1 = 57, so IQR=67 - 57 = 10.

Step8: Determine the interval with the most data

The second quartile (57 - 61) represents the middle 25% of the data. In a box - and - whisker plot, the box (which contains the second and third quartiles) represents 50% of the data. The interval 57 - 61 is part of this box and has more data than the other given intervals.

Answer:

a. Second
b. 3
c. First
d. 14
e. 10
f. 57 - 61