The heights of `8` students in a study group are `180` cm, `160` cm, `175` cm, `165` cm , `178` cm, `170` cm, `174` cm and `182` cm. Find their mean height.

Options

A. `183 cm`
B. `173 cm`
C. `179 cm`
D. `153 cm`

Answer

To find the mean height of the 8 students, we will follow these steps:

### Step 1: List the heights
The heights of the students are:
- 180 cm
- 160 cm
- 175 cm
- 165 cm
- 178 cm
- 170 cm
- 174 cm
- 182 cm

### Step 2: Calculate the sum of the heights
We will add all the heights together:
\[ 180 + 160 + 175 + 165 + 178 + 170 + 174 + 182 \]

Calculating this step by step:
- \(180 + 160 = 340\)
- \(340 + 175 = 515\)
- \(515 + 165 = 680\)
- \(680 + 178 = 858\)
- \(858 + 170 = 1028\)
- \(1028 + 174 = 1202\)
- \(1202 + 182 = 1384\)

So, the total sum of the heights is \(1384\) cm.

### Step 3: Count the number of students
The number of students is \(8\).

### Step 4: Calculate the mean
The mean height is calculated by dividing the total sum of heights by the number of students:
\[ \text{Mean} = \frac{\text{Sum of heights}}{\text{Number of students}} = \frac{1384}{8} \]

### Step 5: Perform the division
Now, we will divide \(1384\) by \(8\):
- \(8\) goes into \(13\) once (1), remainder \(5\).
- Bring down \(8\) (making it \(58\)), \(8\) goes into \(58\) seven times (7), remainder \(2\).
- Bring down \(4\) (making it \(24\)), \(8\) goes into \(24\) three times (3), remainder \(0\).

Thus, \(1384 \div 8 = 173\).

### Final Answer
The mean height of the students is \(173\) cm.

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