Question

Find the Mean and Median of the data \[ 11,\ 7,\ 6,\ 9,\ 12,\ 15,\ 19,\ 20 \]

• A. Mean = 12, Median = 11
• B. Mean = 11.5, Median = 12.38
• C. Mean = 12.38, Median = 11.5
• D. Mean = 12.38, Median = 11.00

Hint:

For an even number of observations: \[ \text{Median} = \frac{\left(\frac{n}{2}\right)^{th}+\left(\frac{n}{2}+1\right)^{th}}{2} \]

Answer 1

The Correct Option is C

Step 1: Calculate the mean.
\[ 11+7+6+9+12+15+19+20 = 99 \] Number of observations: \[ n=8 \] Therefore, \[ \text{Mean} = \frac{99}{8} = 12.375 \] \[ \approx 12.38 \]

Step 2: Arrange the data.
\[ 6,\ 7,\ 9,\ 11,\ 12,\ 15,\ 19,\ 20 \]

Step 3: Find the median.
Since \(n=8\) is even, \[ \text{Median} = \frac{11+12}{2} \] \[ = 11.5 \]

Step 4: Answer.
\[ {\text{Mean}=12.38} \] \[ {\text{Median}=11.5} \] Hence, \[ {\text{Option (C)}} \]