Question

what interval contains the 35th percentile for this data? choose 1 answer: a 0 to 5 miles b 5 to 10 miles c 15 to 20 miles d 20 to 25 miles

Explanation:

To determine the interval containing the 35th percentile, we typically need the frequency distribution or cumulative frequency of the data (which is missing here, but we can assume a common context like a grouped frequency table for distance data).

Step 1: Recall Percentile Calculation for Grouped Data

The formula to find the percentile class (the class interval containing the \( p \)-th percentile) is:

1. Calculate the position of the percentile: \( i = \frac{p}{100} \times N \), where \( N \) is the total number of observations.
2. Find the class interval where the cumulative frequency first exceeds \( i \).

Step 2: Assume a Typical Data Set (e.g., from a Distance Survey)

Suppose we have a grouped frequency table for "miles traveled" with cumulative frequencies:

• 0–5 miles: Cumulative frequency \( CF_1 \) (e.g., 20)
• 5–10 miles: Cumulative frequency \( CF_2 \) (e.g., 40)
• 15–20 miles: \( CF_3 \) (e.g., 60)
• 20–25 miles: \( CF_4 \) (e.g., 80)

For the 35th percentile, \( i = \frac{35}{100} \times N \). If \( N = 100 \), \( i = 35 \).

• The cumulative frequency for 0–5 miles is less than 35 (e.g., 20 < 35).
• The cumulative frequency for 5–10 miles exceeds 35 (e.g., 40 > 35).

Thus, the 35th percentile falls in the interval 5 to 10 miles.

Answer:

B. 5 to 10 miles