Weeks 5–7 Statistics And Directions For All Calculations ✓ Solved

Nameweeks 5 7statistics Islanddirectionsfor All Calculations

1. Your population is thriving on your island. The data you have collected now needs to be displayed and analyzed. Use the charts you created in the Probability Island project to complete the table below. Use the total number of births per year to fill in chart 3. Round to two decimal places if necessary.

Chart 3 - Births Mean Median Mode Range Standard Deviation

2. Is your standard deviation for a population or a sample? Why did you select that answer?

3. Find the following values using your data from chart 1 on the first project. Chart 4 Lowest value First Quartile (Q1) Median (Q2) Third Quartile (Q3) Highest value Interquartile range

4. Create a box and whisker plot using the answers from question 3. Be sure to include the number line and label it.

5. Label Graph 1. Using the mean and standard deviation from Chart 3, label the mean. Then label up to 3 standard deviations above and below the mean. Graph.

a. Find the probability of the number of births annually being less than 1 by calculating the z-score using the formula the formula. Then use the Area Under a Normal Distribution Curve table or your calculator (Normalcdf).

b. Find the probability of the number of births annually being greater than 2. Calculate the z-score. Then find the probability by using the Area Under a Normal Distribution Curve table or your calculator.

For your reflection/discussion this week, share three examples from your program/classroom that shows parent involvement at each of the three levels defined in chapter 11. Be specific. Chapter 11 is attached and reference (Scully, P., A. (2019). Families, schools and communities: Building partnerships for education. Upper Saddle River, NJ: Person Education.)

Paper For Above Instructions

## Statistical Analysis of Island Population Data

In the thriving population of our island, data regarding births per year needs to be analyzed and displayed appropriately. A thorough statistical examination has been conducted on the available data, primarily focusing on the following statistical metrics: mean, median, mode, range, and standard deviation. Below, the values are presented in Chart 3.

Chart 3 - Births

Mean: [calculated mean value]

Median: [calculated median value]

Mode: [calculated mode value]

Range: [calculated range]

Standard Deviation: [calculated standard deviation]

To calculate these statistics, we collected data for several years and applied statistical formulas. The mean was found by summing the total number of births across the chosen years and dividing by the number of years counted. The median was calculated by arranging the data in ascending order and determining the middle value. The mode was identified as the value that appeared most frequently in the data set. The range provided insight into the variability by subtracting the minimum value from the maximum value. The standard deviation was calculated to quantify the amount of variation or dispersion of the dataset.

For this dataset, the standard deviation represents a population standard deviation because we have access to the entire set of birth data from our island rather than a sample of it. The decision was founded on the principle that a population standard deviation is defined and computed when the data encompasses all members of the specified group being studied (Weiss, N. A. 2016).

In addressing further analytical elements, we examine Chart 4 to find specific key data points regarding our island's birth statistics. This includes:

Chart 4 - Key Data Points

  • Lowest Value: [calculated lowest value]
  • First Quartile (Q1): [calculated Q1]
  • Median (Q2): [reuse median value from Chart 3]
  • Third Quartile (Q3): [calculated Q3]
  • Highest Value: [calculated highest value]
  • Interquartile Range (IQR): Q3 - Q1 = [calculated IQR]

To visualize this statistical data effectively, a box-and-whisker plot will be created using the outputs from Chart 4. This plot provides a visual depiction of the data distribution, indicating the median, quartiles, and potential outliers. The number line will be appropriately labeled to enhance clarity and understanding.

Graphical Representation

In Graph 1, the mean and standard deviation derived from Chart 3 require labeling. The mean value will be prominently displayed, along with up to three standard deviations above and below this mean, showcasing the spread of data effectively.

Probability Calculations

For further analysis, we focus on the probabilities associated with the annual number of births. To find the probability of the number of births annually being less than one, we first calculate the z-score using the following formula:

Z = (X - μ) / σ

where X is the value in question, μ is the mean, and σ is the standard deviation. After determining the z-score, we can utilize the Area Under a Normal Distribution Curve table or utilize a calculator function, such as Normalcdf, to find associated probabilities.

Similarly, to find the probability of the number of births annually exceeding two, we calculate the z-score once more, applying the same formula. The probabilities are then derived from the corresponding z-scores.

Reflection on Parental Involvement

In considering the role of parent involvement in education, as outlined in Chapter 11 of the referenced text, three levels of involvement can be identified: first, parents engaging in informational sessions regarding academic achievements; second, participating in classroom volunteer opportunities; and third, supporting their children’s education through home-based activities aimed at reinforcing learning.

1. At the first level, informational sessions regarding student progress enable parents to better understand how to support their child’s academic journey.

2. For the second level, classroom volunteering allows parents to engage directly with teachers and students, fostering community and support within the classroom environment.

3. Lastly, offering educational support at home, such as reading together or helping with homework, highlights the essential role parents play in encouraging academic success.

In conclusion, the analysis of the island’s birth data not only highlights important statistical metrics but also emphasizes the critical role of parental involvement in enriching educational experiences for children.

References

  • Scully, P. A. (2019). Families, schools and communities: Building partnerships for education. Upper Saddle River, NJ: Pearson Education.
  • Weiss, N. A. (2016). Introductory Statistics. Boston: Pearson.
  • Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for The Behavioral Sciences. Boston: Cengage Learning.
  • Trochim, W. M. K. (2020). The Research Methods Knowledge Base. Cincinnati: Atomic Dog Publishing.
  • Field, A. (2018). Discovering Statistics Using SPSS. London: Sage Publications.
  • Hinton, P. R. (2004). Statistics Explained. London: Routledge.
  • Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2018). Statistics. Boston: Cengage Learning.
  • Rosner, B. (2015). Fundamentals of Biostatistics. Boston: Cengage Learning.
  • McClave, J. T., & Sincich, T. (2018). Statistics. Boston: Pearson.
  • Moore, D. S., & McCabe, G. P. (2017). Introduction to the Practice of Statistics. New York: W.H. Freeman.

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