Select five random numbers between 70 and 100. Calculate the mean, median, mode, and midrange of these numbers. Based on your calculations, which measure of central tendency best represents these numbers?
OK, so selecting five numbers at random, I will use:
75, 76, 83, 91, 87
Mean: (75 + 76 + 83 + 91 + 87)/5 = 82.4
Median: is the middle number, so 83.
Mode: is the number which repeats the most, so since no numbers repeat, there is no mode.
Midrange: is the average of the highest and the lowest, so: (75 + 91)/2 = 83.
Since the actual average, median, and midrange of the POPULATION (that is, all numbers from 70 to 100) is 85, we see that the measurements in our calculation that gets us closest is the median and the midrange, both at 83. The mean is also close at 82.4, but not as close as the other two.
You should repeat this exercise with your own random numbers to make sure you understand what we did above and see if your results differ.
Hope that helps =)
thanks- it helped me understand my homework.
To select five random numbers between 70 and 100, you can use a random number generator or manually choose numbers within that range. Let's assume we get the following numbers: 73, 86, 95, 71, and 91.
To calculate the mean, you need to sum up all the numbers and divide the sum by the total count. In this case: (73 + 86 + 95 + 71 + 91) / 5 = 416 / 5 = 83.2.
To find the median, you need to arrange the numbers in ascending order: 71, 73, 86, 91, 95. Since there is an odd number of numbers, the median is the middle value, which in this case is 86.
To identify the mode, you need to determine which value appears most frequently. In this example, there is no number that appears more than once, so there is no mode.
The midrange is the average of the minimum and maximum values. In this case, the minimum is 71 and the maximum is 95. So the midrange is (71 + 95) / 2 = 166 / 2 = 83.
Based on these calculations, we can see that the mean, median, and midrange are all very close together, all around 83. This suggests that these values are evenly distributed, and all three measures of central tendency accurately represent the data. In this case, any of these measures can be considered the best representation of the data.