The monthly rents for the apartments in a building are listed below. $425, $550, $550, $550, $650, $650, $650, $650, $800, $900
Part A: Find the mean, median, mode, range, and standard deviation of the rents.
Part B: The apartment manager considers raising the rent for every apartment by $50. Find the mean, median, mode, range, and standard deviation of the rents after they are raised by $50. Explain your reasoning.
Part C: The apartment manager then decides to raise the rent for every apartment by 10% instead of raising each rent by $50. Find the mean, median, mode, range, and standard deviation of the rents after they are raised by 10%. Compare these with the values calculated in Part B. Explain any differences.
Range = highest value - lowest=$475
Mode = most frequently occurring score=$650
Median = 50th percentile. Half of the scores have a higher value and half are lower=$650
Mean = sum of scores/number of scores=$637.50
To find the mean, median, mode, range, and standard deviation of the rents, you will need to perform some calculations. Let's go through each part step by step.
Part A:
To find the mean, you need to add up all the rents and divide by the total number of rents.
Mean = (425 + 550 + 550 + 550 + 650 + 650 + 650 + 650 + 800 + 900) / 10 = 635
To find the median, you need to arrange the rents in ascending order and find the middle value.
Arranged rents: 425, 550, 550, 550, 650, 650, 650, 650, 800, 900
Median = 650
The mode is the value that appears most frequently in a set of data.
Mode = 650 (since it appears 4 times, which is more than any other rent)
The range is the difference between the largest and smallest values in a set of data.
Range = 900 - 425 = 475
To find the standard deviation, you need to calculate the square root of the variance. First, calculate the variance by finding the average of the squared differences from the mean.
Variance = [(425 - 635)^2 + (550 - 635)^2 + (550 - 635)^2 + (550 - 635)^2 + (650 - 635)^2 + (650 - 635)^2 + (650 - 635)^2 + (650 - 635)^2 + (800 - 635)^2 + (900 - 635)^2] / 10
Variance = 27860 / 10 = 2786
Then, take the square root of the variance to find the standard deviation.
Standard deviation = sqrt(2786) ≈ 52.78
Part B:
To find the mean, you need to add $50 to each rent and then calculate the new mean.
Mean = (425 + 550 + 550 + 550 + 650 + 650 + 650 + 650 + 800 + 900 + 50*10) / 10 = 685
Since adding $50 to each rent increases all the values equally, the median, mode, and range will remain the same as in Part A.
The standard deviation, however, will change. To calculate the new standard deviation, you will need to recalculate the variance using the new rents.
Part C:
To find the mean, you need to increase each rent by 10% and then calculate the new mean.
Mean = (425 + 550*1.1 + 550*1.1 + 550*1.1 + 650*1.1 + 650*1.1 + 650*1.1 + 650*1.1 + 800*1.1 + 900*1.1) / 10 ≈ 697.5
Since increasing each rent by 10% will change the values but not the order, the median and range will change.
The mode will remain the same as it represents the value that appears most frequently.
To calculate the new standard deviation, you will need to recalculate the variance using the new rents.
The main difference between Part B and Part C is in how the rent increase is applied. In Part B, each rent is increased by $50, which results in an equal increase for all rents. In Part C, each rent is increased by 10%, which leads to a different proportional increase for each rent. This results in a greater change in the overall values, including the mean and standard deviation, compared to Part B.
Range = highest value - lowest
Mode = most frequently occurring score
Median = 50th percentile. Half of the scores have a higher value and half are lower.
Mean = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
I'll let you do the calculations.