Question

for exercises 1 and 2, use the description to answer the questions. yuzuki surveyed her teammates about the number of miles they run each day. their responses were 2, 4, 1, 3, 3, 5, 2, 2, 4, 3, and 6 miles. 1. what is the range and interquartile range of the data? 2. what do the range and interquartile range tell you about the number of miles yuzuki’s teammates run each day?

Explanation:

Step1: Arrange data in ascending order

1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6

Step2: Calculate the range

Range = Maximum - Minimum. Maximum = 6, Minimum = 1. So Range = 6 - 1 = 5

Step3: Find the median (Q2)

There are 11 data - points. The median is the 6th value. So Q2 = 3

Step4: Find Q1

The lower half of the data is 1, 2, 2, 2, 3. The median of the lower half (Q1) is 2

Step5: Find Q3

The upper half of the data is 3, 4, 4, 5, 6. The median of the upper half (Q3) is 4

Step6: Calculate the inter - quartile range (IQR)

IQR = Q3 - Q1 = 4 - 2 = 2

The range of 5 indicates the overall spread of the data, meaning the difference between the maximum and minimum number of miles run. The inter - quartile range of 2 shows the spread of the middle 50% of the data. It implies that the middle half of Yuzuki's teammates' daily running distances vary by 2 miles.

Answer:

Range: 5; Inter - quartile range: 2