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The median for the given set of six ordered data values is 26.5 . 91221 _ 4149 What is the missing value? The missing value is ◻.

The median for the given set of six ordered data values is 2626.55 .\newline91221_4149 91221 \_4149 \newlineWhat is the missing value?\newlineThe missing value is □ \square .

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Full solution

Q. The median for the given set of six ordered data values is 2626.55 .\newline91221_4149 91221 \_4149 \newlineWhat is the missing value?\newlineThe missing value is □ \square .
  1. Understand Median Concept: To find the missing value in an ordered set with a median of 26.526.5, we first need to understand that the median is the middle number in a sorted list of numbers. Since we have 66 data values, the median will be the average of the third and fourth numbers when the data is ordered from least to greatest.
  2. Identify Missing Value Position: We are given the ordered set as 9,12,21,_,41,499, 12, 21, \_, 41, 49. The missing value is the fourth number in this list because the third and fourth numbers are the middle two numbers in a set of six.
  3. Set Up Equation for Median: To find the median, we need to average the third and fourth numbers. We are told that the median is 26.526.5. Therefore, we can set up the equation (21+missing value)/2=26.5(21 + \text{missing value})/2 = 26.5 to find the missing value.
  4. Solve for Missing Value: Now we solve for the missing value: Multiply both sides of the equation by 22 to get rid of the fraction: 21+missing value=5321 + \text{missing value} = 53.
  5. Isolate Missing Value: Subtract 2121 from both sides to isolate the missing value: missing value =53−21= 53 - 21.
  6. Perform Subtraction: Perform the subtraction: missing value=32\text{missing value} = 32.

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