You work for a large farm with many fields of corn. You are investigating the mass of a sample of ears of corn. You gather the following data and enter it into your **spreadsheet**:

Mass(g) of ears of corn

13.9

18.2

14.8

17.0

19.1

15.7

18.5

12.7

15.5

38.6

18.1

18.5

14.0

21.8

29.3

12.7

19.6

19.1

13.6

19.0

15.0

17.0

13.8

15.1

To investigate this data further, let's go through some useful calculations that can help analyze the mass of these ears of corn:

### 1. **Mean (Average) Mass**:
   The mean gives us the average mass of the sample.

   \[
   \text{Mean} = \frac{\sum \text{Masses}}{\text{Number of entries}}
   \]

### 2. **Median Mass**:
   The median is the middle value when the masses are ordered from smallest to largest. If there is an even number of values, the median will be the average of the two middle numbers.

### 3. **Range**:
   The range is the difference between the largest and smallest mass in the dataset.

   \[
   \text{Range} = \text{Maximum mass} - \text{Minimum mass}
   \]

### 4. **Standard Deviation**:
   This will tell us how spread out the masses are from the mean.

   \[
   \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{n}}
   \]

   Where \( x_i \) represents each individual mass, \( \mu \) is the mean, and \( n \) is the number of entries.

### 5. **Outliers**:
   We can detect outliers by using the Interquartile Range (IQR). Any mass that is significantly higher or lower than the typical range (e.g., 1.5 times the IQR) might be an outlier.

   - Calculate the first quartile (Q1) and third quartile (Q3).
   - Compute the IQR: \( \text{IQR} = Q3 - Q1 \).
   - Outliers: Any values below \( Q1 - 1.5 \times \text{IQR} \) or above \( Q3 + 1.5 \times \text{IQR} \).

Would you like me to calculate these statistics for you, or guide you through any specific analysis? 

Here are 5 related questions:
1. What are the possible implications of outliers in this corn mass data?
2. How could standard deviation help in understanding the variation in corn mass?
3. What is the significance of the range in the context of this dataset?
4. How would the results change if one of the large or small masses is removed from the dataset?
5. How can the median be more useful than the mean in skewed data?

**Tip**: Always check for outliers before interpreting the average, as they can heavily influence the result.

You work for a large farm with many fields of corn. You are investigating the mass of a sample of ears of corn. You gather the following data and enter it into your spreadsheet: Mass(g) of ears of corn: 13.9, 18.2, 14.8, 17.0, 19.1, 15.7, 18.5, 12.7, 15.5, 38.6, 18.1, 18.5, 14.0, 21.8, 29.3, 12.7, 19.6, 19.1, 13.6, 19.0, 15.0, 17.0, 13.8, 15.1

Learn how to analyze the mass of corn ears using statistical methods. This includes calculating the mean, median, range, and standard deviation. Data includes 24 mass measurements ranging from 12.7g to 38.6g, providing a real-world example of statistical analysis. Suitable for Grades 9-12 students.

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