Question:
If the mean of the observations k, (k+8), (2k-1), (k+12), 12 and 17 is 13, then find the median of these observations.
If the mean of the observations k, (k+8), (2k-1), (k+12), 12 and 17 is 13, then find the median of these observations.
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For even n, median = average of middle two terms
Updated On: Apr 21, 2026
- 11
- 14.5
- 12.5
- 13
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The Correct Option is D
Solution and Explanation
Step 1: Write the sum of all observations.
Sum = \(k + (k+8) + (2k-1) + (k+12) + 12 + 17\).
Combine like terms: \(k + k + 2k + k = 5k\).
Constants: \(8 - 1 + 12 + 12 + 17 = 48\).
Sum = \(5k + 48\). Step 2: Use the mean formula.
Mean = \(\frac{5k + 48}{6} = 13\).
\(5k + 48 = 78\).
\(5k = 30\).
\(k = 6\). Step 3: List all observations.
\(k = 6\), \(k+8 = 14\), \(2k-1 = 11\), \(k+12 = 18\), 12, 17.
Set: \(\{6, 14, 11, 18, 12, 17\}\). Step 4: Sort the observations.
Sorted: \(6, 11, 12, 14, 17, 18\).
Number of observations \(n = 6\) (even). Step 5: Compute median.
Median = average of \(\frac{n}{2}\)th and \(\frac{n}{2}+1\)th terms.
= average of 3rd term (12) and 4th term (14).
= \(\frac{12 + 14}{2} = 13\).
Sum = \(k + (k+8) + (2k-1) + (k+12) + 12 + 17\).
Combine like terms: \(k + k + 2k + k = 5k\).
Constants: \(8 - 1 + 12 + 12 + 17 = 48\).
Sum = \(5k + 48\). Step 2: Use the mean formula.
Mean = \(\frac{5k + 48}{6} = 13\).
\(5k + 48 = 78\).
\(5k = 30\).
\(k = 6\). Step 3: List all observations.
\(k = 6\), \(k+8 = 14\), \(2k-1 = 11\), \(k+12 = 18\), 12, 17.
Set: \(\{6, 14, 11, 18, 12, 17\}\). Step 4: Sort the observations.
Sorted: \(6, 11, 12, 14, 17, 18\).
Number of observations \(n = 6\) (even). Step 5: Compute median.
Median = average of \(\frac{n}{2}\)th and \(\frac{n}{2}+1\)th terms.
= average of 3rd term (12) and 4th term (14).
= \(\frac{12 + 14}{2} = 13\).
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