To solve the problem step by step, we will find the Median, Mean, and Mode of the given marks of 13 students.
### Given Marks:
31, 37, 29, 41, 35, 35, 38, 36, 35, 38, 32, 29, 43
### Step 1: Arrange the data in ascending order
First, we need to arrange the marks in ascending order.
**Ascending Order:**
29, 29, 31, 32, 35, 35, 35, 36, 37, 38, 38, 41, 43
### Step 2: Find the Median
The median is the middle value of the data set. Since there are 13 values (an odd number), the median will be the value at the position (n + 1) / 2, where n is the number of observations.
**Calculation:**
- Number of observations (n) = 13
- Position of median = (13 + 1) / 2 = 14 / 2 = 7
The 7th value in the ordered list is 35.
**Median = 35**
### Step 3: Find the Mean
The mean is calculated by adding all the values together and dividing by the number of observations.
**Calculation:**
1. Sum of all observations:
\( 29 + 29 + 31 + 32 + 35 + 35 + 35 + 36 + 37 + 38 + 38 + 41 + 43 = 459 \)
2. Number of observations = 13
3. Mean = Total Sum / Number of Observations
\( Mean = 459 / 13 = 35.3076923077 \)
Rounding to two decimal places, we get:
**Mean ≈ 35.31**
### Step 4: Find the Mode
The mode is the value that appears most frequently in the data set.
**Observation:**
- The number 35 appears 3 times.
- The number 29 appears 2 times.
- The number 38 appears 2 times.
Since 35 appears the most frequently, we have:
**Mode = 35**
### Final Answers:
(a) Median = 35
(b) Mean ≈ 35.31
(c) Mode = 35
---
