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Part 1

Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange for the given sample data. 

An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed below are the phenotype codes where 

1 equals smooth dash yellow1=smooth-yellow​, 

2 equals smooth dash green2=smooth-green​, 

3 equals wrinkled dash yellow3=wrinkled-yellow​, 

and 

4 equals wrinkled dash green4=wrinkled-green. 

Do the results make​ sense?

11

22

44

33

33

33

11

22

33

11

33

22

33

11
 
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Part 1

​(a) The mean phenotype code is 

Let's begin by calculating the mean, median, mode, and midrange for the given sample data. The phenotype codes provided are:

\[ 1, 2, 4, 3, 3, 3, 1, 2, 3, 1, 3, 2, 3, 1 \]

### Step 1: Calculate the Mean
The mean is calculated by summing all the data values and then dividing by the total number of values.

\[
\text{Sum of the data values} = 1 + 2 + 4 + 3 + 3 + 3 + 1 + 2 + 3 + 1 + 3 + 2 + 3 + 1 = 32
\]
\[
\text{Number of data values} = 14
\]
\[
\text{Mean} = \frac{\text{Sum of the data values}}{\text{Number of data values}} = \frac{32}{14} \approx 2.29
\]

### Step 2: Calculate the Median
The median is the middle value when the data set is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers.

Ordered data set: 
\[ 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4 \]

Since there are 14 values (an even number), the median is the average of the 7th and 8th values:
\[ 
\text{7th value} = 2 
\]
\[ 
\text{8th value} = 3 
\]
\[ 
\text{Median} = \frac{2 + 3}{2} = 2.5
\]

### Step 3: Calculate the Mode
The mode is the value that appears most frequently in the data set.

In this data set, the number 3 appears most frequently (six times). So:
\[ 
\text{Mode} = 3
\]

### Step 4: Calculate the Midrange
The midrange is calculated by taking the average of the maximum and minimum values in the data set.

\[
\text{Minimum value} = 1
\]
\[
\text{Maximum value} = 4
\]
\[
\text{Midrange} = \frac{\text{Minimum value} + \text{Maximum value}}{2} = \frac{1 + 4}{2} = 2.5
\]

### Summary
- **Mean**: \( \approx 2.29 \)
- **Median**: \( 2.5 \)
- **Mode**: \( 3 \)
- **Midrange**: \( 2.5 \)

### Do the results make sense?
The data represents categorical variables (phenotype codes), which are typically nominal in nature. While calculating the mode is appropriate, the mean, median, and midrange calculations might not be as meaningful because they assume the data are interval or ratio in nature, which isn't the case here.

---

Do you want more details or have any questions?  
Here are five related questions you might find helpful:

1. Why might calculating the mean for categorical data be inappropriate?
2. What is the difference between nominal and ordinal data?
3. Can you calculate variance or standard deviation for this type of data?
4. What is the significance of the mode in categorical data?
5. How do different levels of measurement affect the types of analysis that can be performed?

**Tip:** For categorical data like phenotype codes, the mode is usually the most informative measure of central tendency.

Learn how to calculate the mean, median, mode, and midrange for a set of phenotype codes. Understand the statistical measures applied to categorical data with a detailed example. Suitable for students in Grades 9-12.

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