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Find the median for the following:

(i) 72, 76, 64, 80, 68, 61, 85, 91, 62, 82
(ii) 58, 54, 21, 51, 59, 46, 65, 31, 68, 41, 36
(iii) 28.8, 20.6, 39.3, 42.6, 40.2, 28.8, 29.7, 30.2, 40.2.

Answer :

To find the median of a data set, follow these steps:

  1. Order the data set in ascending order. The median is the middle value of the ordered list. If the data set has an odd number of observations, the median is the middle number. If it has an even number of observations, the median is the average of the two middle numbers.

Let's calculate the median for each part of the question:

(i) 72, 76, 64, 80, 68, 61, 85, 91, 62, 82:

  • First, order the numbers: 61, 62, 64, 68, 72, 76, 80, 82, 85, 91.
  • This set has 10 numbers, which is even, so we take the 5th and 6th numbers: 72 and 76.
  • The median is the average of 72 and 76:

[tex]\text{Median} = \frac{72 + 76}{2} = \frac{148}{2} = 74[/tex]

(ii) 58, 54, 21, 51, 59, 46, 65, 31, 68, 41, 36:

  • Order the numbers: 21, 31, 36, 41, 46, 51, 54, 58, 59, 65, 68.
  • This set has 11 numbers, which is odd, so the median is the 6th number:

[tex]\text{Median} = 51[/tex]

(iii) 28.8, 20.6, 39.3, 42.6, 40.2, 28.8, 29.7, 30.2, 40.2:

  • Order the numbers: 20.6, 28.8, 28.8, 29.7, 30.2, 39.3, 40.2, 40.2, 42.6.
  • This set has 9 numbers, which is odd, so the median is the 5th number:

[tex]\text{Median} = 30.2[/tex]

The median provides a central point that divides the data set into two equal halves and is useful in understanding the distribution of the data.

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