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Activity C.1.1 Identify and compute the appropriate measures of central tendency using the step-by-step process of the following. Please include to answer the measures of dispersion (Range, Variance and Standard Deviation)

2.Find out the average cholesterol level of 7 sample patients (155, 220, 134, 216, 200, 144 and 191) Cholesterol is related to heart health. Understanding this average helps doctors know how to keep their patients healthy.

Let's solve the problem step-by-step by first identifying and computing the **measures of central tendency** and then moving on to the **measures of dispersion** for the cholesterol levels of the 7 patients.

### Given Cholesterol Levels:
155, 220, 134, 216, 200, 144, 191

### Measures of Central Tendency:

1. **Mean (Average):**
   \[
   \text{Mean} = \frac{\sum \text{Cholesterol Levels}}{n}
   \]
   Where \(n = 7\) (the number of patients).

   \[
   \text{Mean} = \frac{155 + 220 + 134 + 216 + 200 + 144 + 191}{7}
   \]
   \[
   \text{Mean} = \frac{1260}{7} = 180
   \]

   So, the **mean cholesterol level** is 180.

2. **Median (Middle value when data is ordered):**
   First, arrange the values in ascending order:  
   134, 144, 155, 191, 200, 216, 220

   Since there are 7 values (odd number of values), the median is the middle value, which is the 4th value in the ordered list:  
   \[
   \text{Median} = 191
   \]

3. **Mode (Most frequent value):**
   Since all values are unique, there is **no mode** for this dataset.

### Measures of Dispersion:

1. **Range:**
   The range is the difference between the highest and lowest values in the dataset.
   \[
   \text{Range} = \text{Max} - \text{Min} = 220 - 134 = 86
   \]

2. **Variance:**
   Variance is the average of the squared differences from the mean. We first calculate the differences of each value from the mean, square them, and then find the average.

   \[
   \text{Variance} = \frac{\sum (\text{Cholesterol Level} - \text{Mean})^2}{n}
   \]
   \[
   \text{Variance} = \frac{(155-180)^2 + (220-180)^2 + (134-180)^2 + (216-180)^2 + (200-180)^2 + (144-180)^2 + (191-180)^2}{7}
   \]
   \[
   = \frac{(-25)^2 + 40^2 + (-46)^2 + 36^2 + 20^2 + (-36)^2 + 11^2}{7}
   \]
   \[
   = \frac{625 + 1600 + 2116 + 1296 + 400 + 1296 + 121}{7} = \frac{7454}{7} = 1064.86
   \]

   So, the **variance** is approximately **1064.86**.

3. **Standard Deviation:**
   The standard deviation is the square root of the variance:
   \[
   \text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{1064.86} \approx 32.63
   \]

   So, the **standard deviation** is approximately **32.63**.

### Summary:
- **Mean (Average)**: 180
- **Median**: 191
- **Mode**: None
- **Range**: 86
- **Variance**: 1064.86
- **Standard Deviation**: 32.63

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Would you like further clarification on any part of this solution, or do you need more details?

Here are 5 related questions:
1. How would you calculate the mean for a larger dataset?
2. What is the significance of the range in data analysis?
3. Can you explain how variance and standard deviation help understand data variability?
4. What happens to the variance and standard deviation if we increase the sample size?
5. Why is the median sometimes preferred over the mean in measuring central tendency?

**Tip:** When working with small datasets, the mean can be sensitive to outliers. The median is often more robust in such cases.

Find out the average cholesterol level of 7 sample patients (155, 220, 134, 216, 200, 144, and 191). Cholesterol is related to heart health. Understanding this average helps doctors know how to keep their patients healthy.

Learn how to calculate the average cholesterol level for 7 patients (155, 220, 134, 216, 200, 144, 191) and determine measures of dispersion such as range, variance, and standard deviation. This problem explores key statistical concepts suitable for students in Grades 9-12.

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