Question

The weight (in kilogram) of 8 students in a class are given as 56, 48, 53, 55, 49, 52, 46 , 57. The median weight of the students is

• A. 53.5
• B. 53
• C. 52
• D. 52.5

Answer 1

Answer:

D. 52.5

Understanding Median Calculation

The median is the middle value in a dataset when the data is arranged in ascending or descending order. It divides the dataset into two equal halves. It is a measure of central tendency and is less affected by outliers compared to the mean (average).

Steps to find the Median:

1. Arrange the data: First, arrange the given weights in ascending order. The given weights are: 56, 48, 53, 55, 49, 52, 46, 57.
   Arranged in ascending order: 46, 48, 49, 52, 53, 55, 56, 57.

2. Count the number of data points (n): In this case, there are 8 students, so n = 8.

3. Determine if 'n' is odd or even: Here, 'n' (8) is an even number.

4. Calculate the median for even 'n': When 'n' is even, the median is the average of the two middle values. These are the values at positions n/2 and (n/2) + 1 in the ordered dataset.

   • Position 1: n/2 = 8/2 = 4th position.

   • Position 2: (n/2) + 1 = (8/2) + 1 = 4 + 1 = 5th position.

5. Identify the middle values:

   • The 4th value in the ordered list (46, 48, 49, 52, 53, 55, 56, 57) is 52.

   • The 5th value in the ordered list (46, 48, 49, 52, 53, 55, 56, 57) is 53.

6. Calculate the average of the middle values: Median = (Value at 4th position + Value at 5th position) / 2
   Median = (52 + 53) / 2
   Median = 105 / 2
   Median = 52.5