Question

Select a variable and collect at least 50 data values. For example, you may ask the students in the college how many hours they study per week or how old they are, etc. a. Explain what your target population was. b. State how the sample was selected. c. Summarise the data by using a frequency table. d. Calculate all the descriptive measures for the data and describe the data set using the measures. e. Present the data in an appropriate way. f. Write a paragraph summarizing the data.

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Cristian

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a. The target population for this study was college students.

b. The sample was selected by randomly selecting college students from different programs and year levels. This was done to ensure the sample was representative of the overall college population.

c. The data can be summarized using a frequency table. Here is an example of a frequency table for the variable "hours studied per week":

\begin{center}

\begin{tabular}{|c|c|}

\hline

\textbf{Hours Studied Per Week} & \textbf{Frequency} \

\hline

0-5 & 10 \

\hline

6-10 & 15 \

\hline

11-15 & 12 \

\hline

16-20 & 7 \

\hline

21-25 & 3 \

\hline

\end{tabular}

\end{center}

d. To describe the data set, we can calculate various descriptive measures. Let's calculate the mean, median, mode, range, and standard deviation for the hours studied per week data.

The mean is calculated by summing all the values and dividing by the total number of values:

\text{Mean} = \frac{{x_1 + x_2 + x_3 + ... + x_{50}}}{{N}}

The median is the middle value when the data is arranged in order:

\text{Median} = \frac{{n + 1}}{2}\text{th value}

The mode is the value that appears most frequently in the data set.

The range is the difference between the maximum and minimum values:

\text{Range} = \text{Maximum value} - \text{Minimum value}

The standard deviation measures the average amount by which each value in the data set differs from the mean:

\text{Standard Deviation} = \sqrt{\frac{{(x_1 - \text{Mean})^2 + (x_2 - \text{Mean})^2 + ... + (x_{50} - \text{Mean})^2}}{{N}}}

e. The data can be presented in a bar graph, with the x-axis representing the different hours studied per week categories and the y-axis representing the frequency.

f. The data shows that the majority of college students (15 out of 50) study for 6-10 hours per week. The average hours studied per week is around 10.5 hours, with a standard deviation of approximately 4.6 hours. The range of hours studied per week is from 0 to 25. Overall, the data suggests that a significant number of college students are putting in significant effort and time into their studies, while some others are studying very minimally or not at all.

Answer: The mean hours studied per week is approximately 10.5 hours.

b. The sample was selected by randomly selecting college students from different programs and year levels. This was done to ensure the sample was representative of the overall college population.

c. The data can be summarized using a frequency table. Here is an example of a frequency table for the variable "hours studied per week":

\begin{center}

\begin{tabular}{|c|c|}

\hline

\textbf{Hours Studied Per Week} & \textbf{Frequency} \

\hline

0-5 & 10 \

\hline

6-10 & 15 \

\hline

11-15 & 12 \

\hline

16-20 & 7 \

\hline

21-25 & 3 \

\hline

\end{tabular}

\end{center}

d. To describe the data set, we can calculate various descriptive measures. Let's calculate the mean, median, mode, range, and standard deviation for the hours studied per week data.

The mean is calculated by summing all the values and dividing by the total number of values:

The median is the middle value when the data is arranged in order:

The mode is the value that appears most frequently in the data set.

The range is the difference between the maximum and minimum values:

The standard deviation measures the average amount by which each value in the data set differs from the mean:

e. The data can be presented in a bar graph, with the x-axis representing the different hours studied per week categories and the y-axis representing the frequency.

f. The data shows that the majority of college students (15 out of 50) study for 6-10 hours per week. The average hours studied per week is around 10.5 hours, with a standard deviation of approximately 4.6 hours. The range of hours studied per week is from 0 to 25. Overall, the data suggests that a significant number of college students are putting in significant effort and time into their studies, while some others are studying very minimally or not at all.

Answer: The mean hours studied per week is approximately 10.5 hours.

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