The mode of the reported annual household incomes is $15,400, which is the most frequently occurring income. To find the median, the incomes would need to be arranged in ascending order, and since the number of households is even, the median would be the average of the 8th and 9th income figures. The mean is computed by dividing the sum of all incomes by the number of households (16 in this case).
To find the central tendencies—mode, median, and mean—we begin by organizing the data for the annual household incomes provided in the question. Let's address each measure of central tendency one by one.
The mode is the value that appears most frequently in a data set. By looking at the list of incomes, we see that $15,400 appears four times, which is more frequent than any other income figure. Therefore, the mode is $15,400.
To find the median, we need to arrange the incomes in ascending order and then locate the middle number. If there is an even number of observations, the median is the average of the two middle numbers:
Sort the incomes in ascending order.
Count the number of income values to determine if an even or odd number of data points exists.
If it's an even number, calculate the average of the two central numbers.
As the list of income values provided has an even number of incomes (16), the median will be calculated by the average of the 8th and 9th incomes in the ordered list.
Finally, the mean is calculated by adding up all the incomes and dividing by the total number of households. We sum all the listed incomes and then divide by 16, the number of reported incomes.
These measures provide a comprehensive understanding of the income distribution in the neighborhood, which could then be compared to broader income statistics such as the American median household income or the income of households living in poverty as mentioned in the additional information provided.
The probable question may be:
In a neighborhood survey, households reported their annual incomes. Below is a list of some of the reported annual household incomes. Let's explore the central tendencies of the data.
Annual Household Income (in dollars):
15,400,15,400,8,050,18,550,11,800,19,550,23,500,9,850,18,700,24,300,9,450,14,550,21,900,17,500,16,850,18,50015,400,15,400,8,050,18,550,11,800,19,550,23,500,9,850,18,700,24,300,9,450,14,550,21,900,17,500,16,850,18,500
Additional Information:
To understand the income distribution in the neighborhood, we can analyze the data using various statistical measures.
Mode: The mode is the most frequently occurring income in the dataset. What is the mode for the annual household incomes reported by the residents?
Median: The median is the middle value when the incomes are arranged in ascending order. What is the median annual household income for this neighborhood?
Mean: The mean is the average income, calculated by adding up all the incomes and dividing by the number of households. What is the mean annual household income for the surveyed neighborhood?