Find the median and mode respecively of the given data
92, 42, 62, 86, 48, 29, 62, 64, 42, 62, 82

Options

A. 62, 62
B. 42, 42
C. 62, 42
D. 82, 62

Answer

To find the median and mode of the given data set: 92, 42, 62, 86, 48, 29, 62, 64, 42, 62, 82, we will follow these steps:

### Step 1: Arrange the data in ascending order.
First, we need to sort the numbers from smallest to largest.

**Sorted Data:**
29, 42, 42, 48, 62, 62, 62, 64, 82, 86, 92

### Step 2: Find the median.
The median is the middle number of a sorted data set. If there is an odd number of observations, the median is the middle number. If there is an even number of observations, it is the average of the two middle numbers.

**Count the numbers:**
There are 11 numbers in total (which is odd).

**Find the middle position:**
The position of the median can be calculated using the formula:
\[ \text{Median Position} = \frac{n + 1}{2} \]
where \( n \) is the number of observations.

\[ \text{Median Position} = \frac{11 + 1}{2} = \frac{12}{2} = 6 \]

**Identify the median:**
The 6th number in the sorted list is 62.

### Step 3: Find the mode.
The mode is the number that appears most frequently in the data set.

**Count the frequency of each number:**
- 29 appears 1 time
- 42 appears 2 times
- 48 appears 1 time
- 62 appears 3 times
- 64 appears 1 time
- 82 appears 1 time
- 86 appears 1 time
- 92 appears 1 time

**Identify the mode:**
The number that appears most frequently is 62 (it appears 3 times).

### Final Answer:
- **Median:** 62
- **Mode:** 62

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