Questions: What is the median of the following distribution? 26,26,28,29,31,33,35,36,37,38,40,42,43,46,48 A. 56 B. 37 C. 36 D. 33 E. 43

What is the median of the following distribution? 26,26,28,29,31,33,35,36,37,38,40,42,43,46,48 A. 56 B. 37 C. 36 D. 33 E. 43
Transcript text: What is the median of the following distribution? \[ 26,26,28,29,31,33,35,36,37,38,40,42,43,46,48 \] A. 56 B. 37 C. 36 D. 33 E. 43
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Solution

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Solution Steps

Step 1: Data Preparation

The given data set is: \[ 26, 26, 28, 29, 31, 33, 35, 36, 37, 38, 40, 42, 43, 46, 48 \] This data is already sorted in ascending order.

Step 2: Calculate the Median

To find the median, we use the formula for the rank of the median: \[ \text{Rank} = Q \times (N + 1) \] where \( Q = 0.5 \) (for the median) and \( N = 15 \) (the number of data points).

Calculating the rank: \[ \text{Rank} = 0.5 \times (15 + 1) = 0.5 \times 16 = 8.0 \] The rank of \( 8.0 \) indicates that the median is located at the 8th position in the sorted data.

Step 3: Identify the Median Value

The value at the 8th position in the sorted data is: \[ 36 \] Thus, the median of the distribution is \( 36 \).

Final Answer

\(\boxed{36}\)

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