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?
To select five random numbers between 70 and 100, you can use any method you prefer, such as using a random number generator or by randomly selecting numbers within this range. For the sake of explanation, let's say the random numbers are: 72, 85, 92, 71, and 99.
To calculate the mean, you need to find the sum of these numbers and then divide it by the total count. In this case, the sum is 72 + 85 + 92 + 71 + 99 = 419. Dividing 419 by 5 (the count of numbers) gives you a mean of 83.8.
To calculate the median, you need to arrange the numbers in ascending order and find the middle value. In this case, the numbers in ascending order are 71, 72, 85, 92, and 99. Since there is an odd number of values, the median is the middle value, which is 85.
To calculate the mode, you need to determine the value or values that appear most frequently. In this case, there is no mode because each number appears only once.
Finally, the midrange is the average of the lowest and highest numbers. In this case, the lowest number is 71, and the highest number is 99. Adding them up and dividing by 2 gives a midrange of 85.
Considering these calculations, we can see that the measures of central tendency yield different results for this set of numbers. The mean is 83.8, the median is 85, and the midrange is 85. Since the median and midrange coincide, we can say that they best represent these numbers as they are not affected by outliers, unlike the mean. The mean can be influenced by extreme values, which may skew the central tendency.