Ellen also finds the number of siblings for each student in Ms. Nguyen’s class. In this case, she finds that 5 students have no siblings, while 4 students have one sibling, 6 have two siblings, 4 have three siblings, and 5 students have four siblings. Which statement about the two datasets is true? (1 point) Responses Each dataset has the same median, mean, and mode, but the ranges are different. Each dataset has the same median, mean, and mode, but the ranges are different. Each dataset has the same median, mean, and range, but the modes are different. Each dataset has the same median, mean, and range, but the modes are different. Each dataset has the same mean, mode, and range, but the medians are different. Each dataset has the same mean, mode, and range, but the medians are different. Each dataset has the same median, mean, mode, and range.

Answer 1

To determine which statement is true about the two datasets, we need to analyze both datasets: the first being the number of students in Ms. Nguyen’s class, and the second being the number of siblings each student has.

1. Number of Students in Ms. Nguyen’s Class: Not explicitly provided, but we can summarize from Ellen’s findings on the siblings.

   • 5 students with 0 siblings
   • 4 students with 1 sibling
   • 6 students with 2 siblings
   • 4 students with 3 siblings
   • 5 students with 4 siblings

   Total number of students = 5 + 4 + 6 + 4 + 5 = 24 students.

2. Siblings Dataset: The number of siblings each student has can be represented as:

   • 0 (5 times)
   • 1 (4 times)
   • 2 (6 times)
   • 3 (4 times)
   • 4 (5 times)

   Now we compute the median, mean, and mode of the siblings dataset.

   • Mode: The most frequent number of siblings.

     • Mode = 2 siblings (6 students).

   • Range: The difference between the highest and the lowest values.

     • Range = 4 (max) - 0 (min) = 4.

   • Median: The middle value when the data is sorted. To find the median, we list the dataset according to frequency:

     • 0, 0, 0, 0, 0 (5 times)
     • 1, 1, 1, 1 (4 times)
     • 2, 2, 2, 2, 2, 2 (6 times)
     • 3, 3, 3, 3 (4 times)
     • 4, 4, 4, 4, 4 (5 times)

     This gives us: 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4. The median position for 24 data points is between the 12th and 13th values.

     • The 12th value = 2, and the 13th value = 2 → Median = 2.

   • Mean: The average number of siblings.

     • Mean = (05 + 14 + 26 + 34 + 4*5) / 24
     • = (0 + 4 + 12 + 12 + 20) / 24
     • = 48 / 24
     • = 2.

Summarizing:

• Mode = 2
• Median = 2
• Mean = 2
• Range = 4

Without information on the first dataset (number of students in Ms. Nguyen's class), we would have to assume they are the same in their measure of central tendency (mean, median, mode) for the evaluation.

However, based on the sibling data:

• Each dataset has the same median, mean, and mode, but the ranges are different.

From the responses:

• "Each dataset has the same median, mean, and mode, but the ranges are different." is likely the correct answer provided that the other dataset's details matches in median, mean, and mode but has a different range.

Thus, the correct statement regarding the two datasets is: "Each dataset has the same median, mean, and mode, but the ranges are different."