Mean Weight Computation for Patients

The question asks us to compute the mean weight of 8 patients based on their individual weights provided in kilograms. Calculating the mean (or arithmetic average) is a fundamental concept in statistics used to find a central value for a set of numbers.

The mean is computed by adding up all the values in a dataset and then dividing by the total number of values.

Patient Weights Data

The weights of the 8 patients in kilograms are:

• 85 kg
• 109 kg
• 120 kg
• 135 kg
• 158 kg
• 177 kg
• 181 kg
• 195 kg

Formula for Mean Weight

The formula to calculate the arithmetic mean ($\mu$) of a set of values is given by:

$$ \mu = \frac{\sum x}{n} $$

Where:

• $\sum x$ represents the sum of all individual weights.
• $n$ represents the total number of patients (or observations).

Compute Mean Weight Step-by-Step

Let's apply the formula to the given patient weights:

1. Sum of Weights ($\sum x$):

   First, we sum up all the weights of the 8 patients:

   $$ \sum x = 85 + 109 + 120 + 135 + 158 + 177 + 181 + 195 $$

   $$ \sum x = 1160 \text{ kg} $$

2. Number of Patients ($n$):

   There are 8 patients, so $n = 8$.

3. Calculate Mean Weight ($\mu$):

   Now, divide the sum of weights by the number of patients:

   $$ \mu = \frac{1160}{8} $$

   $$ \mu = 145 \text{ kg} $$

Final Mean Weight

The mean weight of the 8 patients is 145 kg. This means that, on average, each patient weighs 145 kilograms.