# Data Representation and Experimental Design This section outlines the principles of representing data variability using error bars and the fundamental components of designing a valid scientific experiment, including groups and variables. ## 1. Sketching Error Bars on Bar Charts Error bars are graphical representations of the variability of data and are used on graphs to indicate the error or uncertainty in a reported measurement. **Purpose:** To show the spread or variability (range or standard deviation) of data points around the mean. **Procedure:** 1. **Calculate error values:** Determine the range or standard deviation for each data set. 2. **Draw bar chart:** Create a bar chart showing the mean value for each category. 3. **Add error bars:** Draw a vertical line centered on each bar, extending up and down by the calculated error value. Caps are often added to the ends. **Range-Based Error Bars:** * The error bar length is half the range. * Formula: $\text{Error bar length} = \frac{\text{Max value} - \text{Min value}}{2}$ **Standard Deviation (SD) Error Bars:** * The error bar length is equal to one standard deviation. * They extend from the mean by $\pm 1 \text{ SD}$. **Example Calculation:** | Category | Data Points | Mean | Range | Standard Deviation (SD) | Length of Error Bars (±SD) | | :------- | :------------------- | :--- | :---- | :---------------------- | :------------------------- | | A | (10, 12, 15, 11, 13) | 12.2 | 5 | 1.92 | ±1.92 | | B | (20, 21, 22, 19, 18) | 20.0 | 4 | 1.58 | ±1.58 | | C | (30, 33, 32, 31, 29) | 31.0 | 4 | 1.58 | ±1.58 | --- ## 2. Experimental Design Designing a valid experiment requires carefully structured groups and clearly defined variables to ensure that the results are reliable and the conclusions are sound. For drawing the bar chart itself, refer to . ### Experimental Groups **Experimental Group:** Also known as the treatment group, this group is exposed to the change or treatment being tested (the independent variable) to observe its effects. * Example: In a fertilizer study, the plants that receive the fertilizer are the experimental group. **Control Group:** This group is kept under normal, unchanged conditions and does not receive the experimental treatment. It serves as a baseline or standard for comparison. * Example: In a fertilizer study, the plants that do not receive fertilizer are the control group. ### Variables in Experiments **Independent Variable:** The factor that the experimenter intentionally changes or manipulates to observe its effect. It is the presumed cause. * An experiment should only have one independent variable to ensure that any observed changes in the dependent variable are due to this factor alone. * Example: The presence or absence of fertilizer. **Dependent Variable:** The factor that is measured or observed in response to changes in the independent variable. It is the effect or outcome. * Dependent variables should be quantitatively measurable. * Example: Plant height, number of leaves, or rate of photosynthesis. **Controlled Variables:** All other factors that are kept constant for both the experimental and control groups. This ensures a fair test by eliminating other potential influences on the outcome. * Also known as constant variables. * Example: Amount of sunlight, water, temperature, soil type, and plant species. --- ## 3. Examples of Experimental Design ### Experiment 1: Effect of Light Intensity on Plant Growth **Objective:** To investigate how different light intensities affect the growth of bean plants. **Hypothesis:** Plants exposed to higher light intensities will grow more than plants under lower light intensities. **Variables:** * **Independent Variable:** Light intensity (e.g., 100%, 75%, 50%, 25%, 10%). * **Dependent Variable:** Plant growth (measured by height in cm and number of leaves). * **Controlled Variables:** Type of plant, soil type, amount of water, temperature, pot size. **Control Group:** The group of plants grown under normal (100%) light intensity. **Diagram of Setup:** ### Experiment 2: Effect of Water Amount on Plant Growth **Objective:** To investigate how the amount of water affects the growth of potato plants. **Hypothesis:** Plants given more water will grow more than plants given less water. **Variables:** * **Independent Variable:** Amount of water per week (e.g., 1000 ml, 800 ml, 600 ml, 400 ml, 200 ml). * **Dependent Variable:** Plant growth (measured by height in cm and number of leaves). * **Controlled Variables:** Type of plant, soil type, light intensity, temperature, pot size. **Control Group:** The group of plants receiving 1000 ml of water per week. ### Experiment 3: Effect of pH on Enzyme Activity **Objective:** To examine how pH affects the activity of the enzyme catalase. **Hypothesis:** Catalase activity will be highest at a neutral pH (pH 7). **Variables:** * **Independent Variable:** pH level (e.g., pH 4, pH 7, pH 10). * **Dependent Variable:** Enzyme activity (measured by the rate of gas production). * **Controlled Variables:** Amount of catalase, amount of hydrogen peroxide, temperature. **Control Group:** The reaction conducted at a neutral pH of 7.

11.5 Sketching Error Bars Based On Range Or Standard Deviation On A Bar Chart | Biostatistics And Data Analyzing | Biology 12