Question

for exercises 3 and 4, use the given information to answer the questions. stem connection a meteorologist is studying the annual rainfall totals, in inches, for a city for 15 years. her observations are shown in the table. 3. describe the variation of the data using the range. 4. what is the interquartile range? what does it describe in this situation? for exercise 5, use the box plot to answer the question.

Explanation:

Step1: Arrange data in ascending order

44, 49, 50, 52, 52, 54, 58, 60, 60, 62, 62, 64, 67, 68, 68

Step2: Calculate the range

The range is the difference between the maximum and minimum values. Maximum value = 68, minimum value = 44. Range = 68 - 44 = 24. It describes the spread between the highest and lowest annual - rainfall amounts in the 15 - year period.

Step3: Find the median (Q2)

Since there are 15 data points, the median is the 8th value. So Q2 = 60.

Step4: Find the lower half and Q1

The lower half of the data is 44, 49, 50, 52, 52, 54, 58. The median of the lower half (Q1) is the 4th value, so Q1 = 52.

Step5: Find the upper half and Q3

The upper half of the data is 62, 62, 64, 67, 68, 68. The median of the upper half (Q3) is the 4th value of this half, so Q3 = 64.

Step6: Calculate the inter - quartile range (IQR)

IQR=Q3 - Q1 = 64 - 52 = 12. The inter - quartile range describes the spread of the middle 50% of the annual rainfall data.

Answer:

1. The range is 24. It shows the difference between the highest and lowest annual rainfall amounts over 15 years.
2. The inter - quartile range is 12. It describes the spread of the middle 50% of the annual rainfall data.