In the United States, the average public school teacher currently earns an annual salary near $55,000. Reported national average salaries for the last six decades are listed below.
Year National
Average
Teachers'
Salary
1960 $4,995
1970 $8,626
1980 $15,970
1990 $31,367
2000 $41,807
2010 $55,202
Use the data represented in the table to answer the following prompts. Answer in complete sentences and include all necessary calculations.
The table used to represent the national average teachers’ salary per decade did not include the data for the year 1950. If the mean national average teachers’ salary per decade for the seven decades is $22,986 per decade, what salary should have been reported for the year 1950? In your final answer, include all of the necessary calculations.
The National Board of Education predicts that the 2020 national census will report the average annual salary of a teacher to be $60,000. Based on the board of education’s prediction, how will the mean, median, and mode of the original data table be affected by the additional data collected in 2020? Note: Do not include data for 1950.
In the United States, the average public school teacher currently earns an annual salary near $55,000. Reported national average salaries for the last six decades are listed below.
Year National
Average
Teachers'
Salary
1960 $4,995
1970 $8,626
1980 $15,970
1990 $31,367
2000 $41,807
2010 $55,202
Create a scatter plot of the data represented in the table of teachers’ salaries. Be sure to include all appropriate labels.
Use the scatter plot created for question #1 to write a line of best fit in the slope-intercept form for the data. In your final answer, include all necessary calculations.
For the equation of the line best fit, predict the national average teachers’ salary for the year 2014. In your final answer, include all necessary calculations.
To determine the best fit undergraduate program, a high school senior researches the majors offered at the universities he is considering for admissions. The internet search reports that Arizona State University lists nine of their most popular majors and the percent of the student population enrolled in the programs.
Popular Majors Percent of Student body
Biology 8%
Business Marketing 20%
Communications/Journalism 6%
Education 5%
Engineering 7%
Interdisciplinary Studies 6%
Psychology 6%
Social Sciences 10%
Visual and Performing Arts 8%
The university’s enrollment is expected to reach at least 22,000 students for the fall semester.
Create a circle graph to represent the university’s expected student enrollment according to major. You may hand draw or use a technology program to create your circle graph.
Create a bar graph to represent the university’s expected student enrollment according to major. You may hand draw or use a technology program to create your bar graph.
1. To find the salary that should have been reported for the year 1950, we need to calculate the sum of the salaries for the six decades and subtract it from the total sum of the seven decades to find the missing average salary. Here's how:
Total sum of the six known decades = $4,995 + $8,626 + $15,970 + $31,367 + $41,807 + $55,202 = $157,967
Total sum of the seven decades = $22,986 * 7 = $160,902
Missing average salary for the year 1950 = Total sum of the seven decades - Total sum of the six known decades = $160,902 - $157,967 = $2,935
Therefore, the salary that should have been reported for the year 1950 is $2,935.
2. The additional data collected in 2020, where the average annual salary of a teacher is predicted to be $60,000, will affect the mean, median, and mode of the original data table. Here's how:
Mean: The mean will increase as the new data point has a higher value than the existing data. The mean will be higher than $22,986.
Median: The median will also increase as the new data point is higher than the previous median.
Mode: The mode will remain unchanged as it represents the salary that occurs most frequently, and the new data point does not affect the mode.
3. To create a scatter plot of the teacher salaries data, plot the year on the x-axis and the corresponding salary on the y-axis. Label the axes as "Year" and "Salary in $". Connect the data points with dots and include a title for the graph.
4. To find the best-fit line for the data, you can use a regression analysis to calculate the slope and y-intercept. However, without specific values, it's not possible to provide the calculations and the equation here. A regression analysis is typically done using software or calculators with statistical functions.
5. With the equation of the best-fit line, you can predict the national average teachers' salary for the year 2014 by substituting 2014 for the year variable in the equation. The result will provide the predicted salary for that year.
6. To create a circle graph representing the university's expected student enrollment according to major, use the percentages provided for each major to calculate the corresponding angle of each sector in the circle. Multiply each percentage by 360 (degrees) to find the angle for that sector. Draw a circle and divide it into sectors, labeling each sector with the major and the corresponding angle. Make sure the sectors add up to 360 degrees.
7. To create a bar graph representing the university's expected student enrollment according to major, use the percentages provided for each major to calculate the corresponding length of each bar. Multiply each percentage by the total number of students (22,000) to find the length of the bar. Draw a horizontal axis indicating the majors and a vertical axis indicating the number of students. For each major, draw a bar with a length corresponding to the calculated value. Include labels for the bars and axis.