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Find the median of the following data: 12, 15, 34, 12, 45, 67, 12, 89, 23, 56.
23
28.5
34
12
28.5
Sort the data mentally by marking smallest to largest and focus only on the middle two values once the count hits n=10. Average these two middle values to get the median.
A set of 10 observations: 12, 15, 34, 12, 45, 67, 12, 89, 23, 56.
Median=2(2nтАЛ)thterm+(2nтАЛ+1)thtermтАЛ
Sort the data mentally by marking smallest to largest and focus only on the middle two values once the count hits n=10. Average these two middle values to get the median.
Students often forget to arrange the numbers in ascending order before calculating the median, leading to incorrect middle-term selection.
Step 1: Arrange data in ascending order
Sort the given 10 observations: 12, 12, 12, 15, 23, 34, 45, 56, 67, 89.
12,12,12,15,23,34,45,56,67,89
Step 2: Identify the number of terms
The total number of observations n is 10, which is an even number.
n=10
Step 3: Apply the median formula for even n
Since n=10, the median is the average of the 5th and 6th terms.
Median=2T5тАЛ+T6тАЛтАЛ
Step 4: Calculate the final value
The 5th term is 23 and the 6th term is 34. Calculating the mean: (23+34)/2=57/2=28.5.
Median=223+34тАЛ=28.5
B is correct because the average of the 5th and 6th terms in the sorted dataset is 28.5.
This concept of central tendency is the foundation for understanding standard deviation and variance in RRB statistics problems.
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