Question:
Given observations
\[
10,4,11,6,17,15,9,8,x
\]
and mean = mode = median. Find the value of \(x\).
Given observations
\[
10,4,11,6,17,15,9,8,x
\]
and mean = mode = median. Find the value of \(x\).
Show Hint
When mean = median = mode, first identify the value that can become the mode and then verify the mean and median conditions.
Updated On: Jun 11, 2026
- \(12\)
- \(10\)
- \(9\)
- \(11\)
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Arrange the observations.
Without \(x\), \[ 4,6,8,9,10,11,15,17. \] To have a mode, one observation must repeat. Among the options, choosing \[ x=10 \] makes 10 occur twice.
Step 2: Find the median.
The ordered data become \[ 4,6,8,9,10,10,11,15,17. \] Since there are 9 observations, the median is the 5th observation. \[ \text{Median}=10. \]
Step 3: Find the mean.
Sum of first eight observations: \[ 4+6+8+9+10+11+15+17=80. \] Adding \(x=10\), \[ \text{Total}=90. \] \[ \text{Mean} = \frac{90}{9} = 10. \] Thus \[ \text{Mean}=\text{Median}=\text{Mode}=10. \] Hence \[ \boxed{x=10}. \]
Without \(x\), \[ 4,6,8,9,10,11,15,17. \] To have a mode, one observation must repeat. Among the options, choosing \[ x=10 \] makes 10 occur twice.
Step 2: Find the median.
The ordered data become \[ 4,6,8,9,10,10,11,15,17. \] Since there are 9 observations, the median is the 5th observation. \[ \text{Median}=10. \]
Step 3: Find the mean.
Sum of first eight observations: \[ 4+6+8+9+10+11+15+17=80. \] Adding \(x=10\), \[ \text{Total}=90. \] \[ \text{Mean} = \frac{90}{9} = 10. \] Thus \[ \text{Mean}=\text{Median}=\text{Mode}=10. \] Hence \[ \boxed{x=10}. \]
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