Question

The mean, median and mode for the data (5, 6, 9, 3, 2, 5, 8, 1, 7, 4) is

• A. 5, 5, 9
• B. 10, 5, 4
• C. 5, 2, 5
• D. 5, 5, 5

Hint:

Always arrange the data in order before finding the median. This is a common mistake. For an even number of data points, remember to take the average of the two central values.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question requires calculating the three main measures of central tendency for a given set of data:

• Mean: The average of all data points.

• Median: The middle value of the dataset when it is arranged in ascending or descending order.

• Mode: The value that appears most frequently in the dataset.

Step 2: Key Formula or Approach:
The data set is: (5, 6, 9, 3, 2, 5, 8, 1, 7, 4).
Number of data points (n) = 10.

Step 3: Detailed Explanation:
1. Calculate the Mean:
The mean is the sum of the values divided by the number of values.
\[ \text{Mean} = \frac{5 + 6 + 9 + 3 + 2 + 5 + 8 + 1 + 7 + 4}{10} = \frac{50}{10} = 5 \] 2. Calculate the Median:
First, arrange the data in ascending order:
1, 2, 3, 4, 5, 5, 6, 7, 8, 9
Since the number of data points (n=10) is even, the median is the average of the two middle values. The middle values are the 5th and 6th terms.
5th term = 5
6th term = 5
\[ \text{Median} = \frac{5 + 5}{2} = \frac{10}{2} = 5 \] 3. Find the Mode:
The mode is the most frequently occurring value in the dataset.
In the set {1, 2, 3, 4, 5, 5, 6, 7, 8, 9}, the number 5 appears twice, while all other numbers appear only once.
Therefore, the Mode is 5.

Step 4: Final Answer:
The mean is 5, the median is 5, and the mode is 5. This matches option (D).