Answer:
Mean of high-cost urban area indices = 185.5
Median of high-cost urban area indices = 180
Range of high-cost urban area indices = 97
Mean of low-cost urban area indices = 77.67
Median of low-cost urban area indices = 76
Range of low-cost urban area indices = 11
Explanation:
Defining the mean:
- The mean is the average of a data set.
- We calculate it by dividing the sum of the data points by the total number of data points.
Defining the median:
- The median is the data point that lies in the middle of a data set arranged in ascending in numerical order.
- Since the median lies in the middle, it has an equal number of data points to the left and right of it.
Defining the range:
- The range is the difference between the smallest and largest value of a data set with the smallest value being subtracting from the largest.
Determining the mean, median, and range of the high-cost urban area living indices:
Finding the mean of the high-cost urban area living indices:
Since there are 6 indices in the high-cost urban area data set, we can find the mean by dividing the sum of the indices by 6:
Mean = (247 + 203 + 202 + 158 + 153 + 150) / 6
Mean = 1113 / 6
Mean = 185.5
Thus, the mean of the high-cost urban area indices is 185.5.
Finding the median of the high-cost urban area living indices:
First, we need to arrange the indices in ascending numerical order.
Thus, we have: 150, 153, 158, 202, 203, 247.
We see that both 158 and 202 lie in the middle of the data set as there are two terms to the left of 158 and 2 terms to the right of 202.
To find the median then, we must average these two values:
Median = (158 + 202) / 2
Median = 360 / 2
Median = 180
Thus, the median of the high-cost urban living area indices is 180.
Finding the range of the high-cost urban area living indices:
Since the highest and lowest high-cost urban area living indices are 247 and 150 respectively, finding the difference of these two numbers will give us the range:
Range = 247 - 150
Range = 97
Thus, the range of the high-cost urban living area indices is 97.
Determining the mean, median, and range of the low-cost urban living indices:
Finding the mean of the low-cost urban area living indices:
Since there are also 6 low-cost urban area living indices, we can find the mean by dividing the sum of these indices by 6:
Mean = (84 + 84 + 77 + 75 + 73 + 73) / 6
Mean = 466 / 6
Mean = 77.66666
Mean = 77.67
Thus, the mean of the low-cost urban area indices is about 77.67.
Finding the median of the low-cost urban area indices:
First, we need to arrange the low-cost urban area indices in ascending numerical order.
Thus, we have: 73, 73, 75, 77, 84, 84
We see that both 75 and 77 lie in the middle of the data set as 73 has two numbers to the left of it and 77 has two numbers to the right of it.
To find the median then, we average these two numbers:
Median = (75 + 77) / 2
Median = 152 / 2
Median = 76
Thus, the median of the low-cost urban area indices is 76.
Finding the range of the low-cost urban area indices:
Since 84 and 73 are the smallest and largest low-cost urban area indices respectively, finding the difference of these two numbers will give us the range:
Range = 84 - 73
Range = 11
Thus, the range of the low-cost urban area indices is 11.