Question Three: The following results are scored in the Principle of Computation and Data Analysis test in a cer academic year, the marks are; \( 7,9,4,5,9,7,5,6 \). Required: 1. Show the steps of Descriptive statistics in SPSS 2. Show the steps of Explore in SPSS 3. Explore the marks 4. Comments on your findings Question Four: Suppose we have the following dataset that shows the average points per game for 16 basketball players: \( 5.00,8.00,8.00,12.00,14.00,15.00,16.00,19.00,20.00,22.00,24.00,25.00,25.00 \), 26.00, \( 30.00,31.00 \) Requirement: 1. Create a stem and leaf plot 2. Show the procedures used in SPSS to create stem and leaf plot 3. Provide different descriptive statistics. 4. Comments on your results

Certainly! Let's address each of your questions step-by-step. We'll start with **Question Three** related to the Principle of Computation and Data Analysis test marks, followed by **Question Four** concerning the basketball players' average points per game. --- ## **Question Three** ### **Given Data:** Marks: 7, 9, 4, 5, 9, 7, 5, 6 ### **1. Steps to Perform Descriptive Statistics in SPSS** **Descriptive Statistics** in SPSS allows you to summarize and describe the main features of a dataset. Here's how you can perform descriptive statistics on the given marks: 1. **Open SPSS and Enter Data:** - Launch SPSS. - In the **Data View**, enter the marks in a single column. For example, name the variable `Marks`. ``` Marks ----- 7 9 4 5 9 7 5 6 ``` 2. **Navigate to Descriptive Statistics:** - Click on `Analyze` in the top menu. - Hover over `Descriptive Statistics`. - Select `Descriptives…` from the dropdown menu. 3. **Select Variables:** - In the **Descriptives** dialog box, select the `Marks` variable from the left box. - Click the arrow button to move it to the **Variables** box on the right. 4. **Choose Statistics to Display:** - Click on the `Options…` button. - In the **Descriptives: Options** dialog, you can select various statistics such as: - Mean - Std. Deviation - Minimum - Maximum - Range - Variance - Select the desired statistics and click `Continue`. 5. **Run the Analysis:** - Click `OK` to execute. - SPSS will generate an output table displaying the selected descriptive statistics for the `Marks` variable. **Sample Output:** | Variable | N | Mean | Std. Deviation | Minimum | Maximum | Range | Variance | |----------|---|------|-----------------|---------|---------|-------|----------| | Marks | 8 | 6.5 | 1.889 | 4 | 9 | 5 | 3.56 | ### **2. Steps to Use the Explore Function in SPSS** The **Explore** function in SPSS provides more detailed descriptive statistics, including measures of distribution, outliers, and graphical representations. 1. **Open SPSS and Enter Data:** - Ensure your data is entered as in Question Three. 2. **Navigate to Explore:** - Click on `Analyze` in the top menu. - Hover over `Descriptive Statistics`. - Select `Explore…` from the dropdown menu. 3. **Assign Variables:** - In the **Explore** dialog box, move the `Marks` variable to the **Dependent List** box. 4. **Specify Display Options:** - (Optional) If you have grouping variables, assign them to the **Factor List**. In this case, since there's only one variable, this step can be skipped. 5. **Choose Plots and Statistics:** - Click on the `Statistics…` button if you want to select additional statistics. - Click on the `Plots…` button to choose graphical representations: - **Boxplot**: Useful for identifying outliers. - **Stem-and-Leaf**: Good for viewing the distribution. - **Histogram** and **Normality Plots**: To visualize the data distribution. - Select desired plots and click `Continue`. 6. **Run the Analysis:** - Click `OK` to execute. - SPSS will generate an output with tables and charts representing the descriptive statistics and distributions for `Marks`. **Sample Output Includes:** - Descriptive Statistics Table - Boxplot - Stem-and-Leaf Plot - Histogram ### **3. Exploration of the Marks** Let's delve into the descriptive statistics and interpret the data. **Descriptive Statistics:** | Statistic | Value | |------------------|-------| | Number of Scores (N) | 8 | | Mean | 6.5 | | Median | 6.0 | | Mode | 5, 7, 9 | | Range | 5 | | Standard Deviation | 1.889 | | Variance | 3.56 | | Minimum | 4 | | Maximum | 9 | **Stem-and-Leaf Plot:** ``` Stem | Leaf 4 | 0 5 | 5,5 6 | 6 7 | 7,7 8 | 9,9 ``` **Boxplot Insights:** - The boxplot shows the distribution of the marks, including the median, quartiles, and any potential outliers. - No significant outliers are present in this dataset. ### **4. Comments on Findings** - **Central Tendency:** - The **mean** mark is **6.5**, while the **median** is **6.0**, indicating a slight positive skewness. - There are multiple modes (5, 7, 9), suggesting that these marks are more frequently occurring. - **Dispersion:** - The **standard deviation** of **1.889** indicates moderate variability in the marks. - The **range** of **5** (from 4 to 9) shows that the marks are spread over a reasonable interval. - **Distribution:** - The **stem-and-leaf plot** illustrates that the marks are fairly evenly distributed across the lower and higher ends with no extreme clustering. - The absence of outliers in the boxplot suggests that all scores are within a typical range for this dataset. - **Implications:** - Most students scored between 5 and 9, with a concentration around the middle scores. - There isn't a significant skew, indicating a balanced performance distribution among students. --- ## **Question Four** ### **Given Data:** Average Points per Game for 16 Basketball Players: 5.00, 8.00, 8.00, 12.00, 14.00, 15.00, 16.00, 19.00, 20.00, 22.00, 24.00, 25.00, 25.00, 26.00, 30.00, 31.00 ### **1. Creating a Stem-and-Leaf Plot** A **Stem-and-Leaf Plot** is a graphical representation that displays data while preserving the original values, making it useful for observing the shape of the distribution. **Stem-and-Leaf Plot for Average Points:** ``` Stem | Leaf 0 | 5 0 | 8,8 1 | 2,4,5,6,9 2 | 0,2,4,5,5,6 3 | 0,1 ``` **Interpretation:** - **Stem** represents the tens place. - **Leaf** represents the units place. - For example, a leaf of 5 under stem 0 represents 5.00 points, while a leaf of 1 under stem 3 represents 31.00 points. ### **2. Procedures to Create a Stem-and-Leaf Plot in SPSS** While SPSS primarily offers various graphical plots like histograms and boxplots, it does not directly support creating stem-and-leaf plots through its standard interface. However, you can create a stem-and-leaf plot using SPSS’s **Custom Tables** or export the data to another software like Excel or use SPSS syntax. Alternatively, you can use the **Text-based** output for simple datasets. Here's how you can approximate a stem-and-leaf plot using SPSS syntax: 1. **Enter Data:** - Open SPSS. - In the **Data View**, enter the average points in a single column, e.g., `AvgPoints`. ``` AvgPoints --------- 5 8 8 12 14 15 16 19 20 22 24 25 25 26 30 31 ``` 2. **Sort the Data:** - To make the plot easier, sort the data in ascending order. - Click on `Data` > `Sort Cases…` - Select `AvgPoints` and click `OK`. 3. **Use Syntax to Create Stem-and-Leaf Plot:** - Click on `File` > `New` > `Syntax`. - Enter the following SPSS syntax: ```spss DISPLAY /STEMLEAF=AvgPoints. ``` - **Note:** SPSS does not have a direct `STEMLEAF` command; instead, you might need to use custom scripts or manual methods. 4. **Alternative Method: Use Frequency Tables:** - Click on `Analyze` > `Descriptive Statistics` > `Frequencies…` - Move `AvgPoints` to the **Variable(s)** box. - Click on the `Charts…` button and select `Histogram` or `Bar Charts`. - Click `Continue`, then `OK`. 5. **Manual Creation (Recommended for Simplicity):** - Given the small dataset, it's efficient to create the stem-and-leaf plot manually as shown above. **Recommendation:** For detailed stem-and-leaf plots, consider using statistical software like Excel or R, or create it manually due to SPSS's limitations in this area. ### **3. Providing Different Descriptive Statistics** **Descriptive Statistics for Average Points:** | Statistic | Value | |------------------------|----------| | Number of Players (N) | 16 | | Mean | 17.44 | | Median | 17.50 | | Mode | 8, 25 | | Range | 26 (31-5)| | Standard Deviation | 8.39 | | Variance | 70.27 | | Minimum | 5.00 | | Maximum | 31.00 | | Skewness | 0.758 | | Kurtosis | -0.646 | **Explanation of Statistics:** - **Mean:** The average points per game is **17.44**. - **Median:** The middle value when the data is ordered is **17.50**, indicating that half the players score below and half above this point. - **Mode:** The most frequently occurring scores are **8 and 25** points. - **Range:** The difference between the highest and lowest scores is **26** points (31 - 5). - **Standard Deviation:** A value of **8.39** shows that the players' points vary moderately around the mean. - **Variance:** The average of the squared deviations from the mean is **70.27**. - **Skewness:** A positive skewness (**0.758**) suggests that the distribution has a longer tail on the right side. - **Kurtosis:** A negative kurtosis (**-0.646**) indicates a flatter distribution than a normal distribution. ### **4. Comments on Results** - **Central Tendency:** - The **mean** (17.44) is slightly higher than the **median** (17.50), which is typical in a positively skewed distribution. - The presence of multiple modes (8 and 25) indicates that there are common scoring points among the players, possibly reflecting different roles or skill levels. - **Dispersion:** - The **standard deviation** of **8.39** signifies a considerable spread in the average points, suggesting diverse performance levels among the players. - A **range** of **26** points (from 5 to 31) further emphasizes the variability in scoring. - **Distribution:** - The **positive skewness** (**0.758**) indicates that while most players score around the lower to middle range, there are a few high scorers that extend the tail to the right. - The **negative kurtosis** (**-0.646**) implies that the data distribution is flatter and has lighter tails compared to a normal distribution, meaning extreme scores are less frequent. - **Implications:** - **Performance Diversity:** The wide range and high standard deviation reflect that player performances vary significantly, which could be due to differences in experience, position, or playing time. - **Strategic Planning:** Coaches might need to tailor training programs to address the wide performance spectrum, ensuring that both lower and higher-performing players are adequately supported. - **Team Composition:** Understanding the distribution helps in making informed decisions about team composition, possibly balancing high scorers with those who excel in other aspects of the game. - **Outliers:** - The highest score (**31.00**) and the lowest score (**5.00**) might be considered outliers, warranting further investigation to understand underlying factors such as player positions, minutes played, or other contributing factors. --- By following these steps and interpretations, you can effectively analyze and comment on both datasets using SPSS and basic statistical principles.