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Consider the following two variables: Frequency 0 2 4 6 8 10 Variable 1 Frequency 02 4 6 8 10 0 2 4 6 8 10 (a) Which variable has the higher standard deviation? O Variable 2 O Variable 1 O They have the same standard deviation 0 2 Variable 2 4 6 8 10 (b) Suppose a new data point at 0 was added in both of the datasets. What would happen to the standard deviations? The standard deviation for Variable 1 would not change The standard deviation for Variable 2 would not change

Consider the following two variables: Frequency 0 2 4 6 8 10 Variable 1 Frequency 02 4 6 8 10 0 2 4 6 8 10 (a) Which variable has the higher standard deviation? O Variable 2 O Variable 1 O They have the same standard deviation 0 2 Variable 2 4 6 8 10 (b) Suppose a new data point at 0 was added in both of the datasets. What would happen to the standard deviations? The standard deviation for Variable 1 would not change The standard deviation for Variable 2 would not change

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 4CYU
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### Understanding Standard Deviation with Histogram Examples Consider the following two variables illustrated in the histograms below: #### Variable 1 ![Histogram for Variable 1](image_url) - Data is represented by a bar histogram. - X-axis: Represents the data points ranging from 0 to 10. - Y-axis: Represents the frequency of each data point. - The distribution appears to be bimodal with peaks around values 2 and 8. #### Variable 2 ![Histogram for Variable 2](image_url) - Data is represented by a bar histogram. - X-axis: Represents the data points ranging from 0 to 10. - Y-axis: Represents the frequency of each data point. - The distribution appears to be unimodal, centered around the value of 5. ### Questions for Analysis **(a) Which variable has the higher standard deviation?** - **Variable 2** - **Variable 1** ⬤ - **They have the same standard deviation** *Hint: Standard deviation measures how spread out the data points are around the mean. More spread implies a higher standard deviation.* **(b) Suppose a new data point at 0 was added to both datasets. What would happen to the standard deviations?** - The standard deviation for Variable 1 would ⬤ **not change**. - The standard deviation for Variable 2 would ⬤ **not change**. *Hint: Adding a data point at 0 to both datasets would either increase the spread, decrease it, or have no impact on standard deviation.* *Note: The above options indicate the analyses selected by the student.* ### Detailed Graph Explanation **Graph for Variable 1:** - The histogram for Variable 1 showcases a bimodal distribution, where two peaks are visible. The bars for values around 2 and 8 are higher, indicating these data points have the highest frequencies. **Graph for Variable 2:** - The histogram for Variable 2 showcases a unimodal distribution, centered around the value 5. Most data points are concentrated around this central value, forming a symmetric shape typically indicative of a normal distribution. ### Conclusion Interpreting histograms and understanding standard deviation is crucial in statistics. Variable 1 likely has a higher standard deviation due to its bimodal nature and wider spread of data points, whereas Variable 2 has a more concentrated spread around its central value. Adding a new data point at 0 would not
Transcribed Image Text:### Understanding Standard Deviation with Histogram Examples Consider the following two variables illustrated in the histograms below: #### Variable 1 ![Histogram for Variable 1](image_url) - Data is represented by a bar histogram. - X-axis: Represents the data points ranging from 0 to 10. - Y-axis: Represents the frequency of each data point. - The distribution appears to be bimodal with peaks around values 2 and 8. #### Variable 2 ![Histogram for Variable 2](image_url) - Data is represented by a bar histogram. - X-axis: Represents the data points ranging from 0 to 10. - Y-axis: Represents the frequency of each data point. - The distribution appears to be unimodal, centered around the value of 5. ### Questions for Analysis **(a) Which variable has the higher standard deviation?** - **Variable 2** - **Variable 1** ⬤ - **They have the same standard deviation** *Hint: Standard deviation measures how spread out the data points are around the mean. More spread implies a higher standard deviation.* **(b) Suppose a new data point at 0 was added to both datasets. What would happen to the standard deviations?** - The standard deviation for Variable 1 would ⬤ **not change**. - The standard deviation for Variable 2 would ⬤ **not change**. *Hint: Adding a data point at 0 to both datasets would either increase the spread, decrease it, or have no impact on standard deviation.* *Note: The above options indicate the analyses selected by the student.* ### Detailed Graph Explanation **Graph for Variable 1:** - The histogram for Variable 1 showcases a bimodal distribution, where two peaks are visible. The bars for values around 2 and 8 are higher, indicating these data points have the highest frequencies. **Graph for Variable 2:** - The histogram for Variable 2 showcases a unimodal distribution, centered around the value 5. Most data points are concentrated around this central value, forming a symmetric shape typically indicative of a normal distribution. ### Conclusion Interpreting histograms and understanding standard deviation is crucial in statistics. Variable 1 likely has a higher standard deviation due to its bimodal nature and wider spread of data points, whereas Variable 2 has a more concentrated spread around its central value. Adding a new data point at 0 would not
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