Answer:
Explanation:
(a) Mean:
To find the mean, we add up all the numbers and then divide by the total number of numbers:
65 + 99 + 5 + 16 + 97 + 69 + 79 + 82 + 86 + 23 + 73 = 694
The total number of numbers is 11.
Mean = sum of all numbers / total number of numbers = 694 / 11 = 63.09 (rounded to two decimal places)
Therefore, the mean is approximately 63.09.
(b) Median:
The median is the middle value when the data is arranged in numerical order. To find the median, we first need to put the numbers in order:
5, 16, 23, 65, 69, 73, 79, 82, 86, 97, 99
Since there are 11 numbers, the median is the middle number, which is 69.
Therefore, the median is 69.
(c) Mode:
The mode is the number that appears most frequently in the data. In this case, there is no number that appears more than once, so there is no mode.
Therefore, there is no mode.
(d) Midrange:
The midrange is the average of the largest and smallest values in the data set. To find the midrange, we first need to find the largest and smallest values:
Smallest value = 5
Largest value = 99
Midrange = (smallest value + largest value) / 2 = (5 + 99) / 2 = 52
Therefore, the midrange is 52.
(e) What do the results tell us?
The results tell us some information about the jersey numbers of 11 players randomly selected from the roster of a championship sports team. Specifically, we know the range of the numbers (5 to 99), the middle number (69), and the average number (approximately 63). However, we cannot make any conclusions about the significance of these numbers without more context about the team and the sport they play.
NOTE:
To find the mean temperature, we need to calculate the weighted average of all the temperatures in the distribution. We can do this by multiplying each temperature by its corresponding frequency, adding up these products, and then dividing by the total frequency.
Using the midpoint of each class interval as a representative value for the temperature, we have:
The midpoint of 40-44 is 42
The midpoint of 45-49 is 47
The midpoint of 50-54 is 52
The midpoint of 55-59 is 57
The midpoint of 60-64 is 62
To calculate the weighted average, we can use the following formula:
mean temperature = (sum of (midpoint * frequency)) / (sum of frequencies)
In this case, the sum of (midpoint * frequency) is:
(42 * 3) + (47 * 5) + (52 * 12) + (57 * 6) + (62 * 3) = 1266
The sum of frequencies is:
3 + 5 + 12 + 6 + 3 = 29
So the mean temperature is:
mean temperature = 1266 / 29 = 43.655
Comparing the computed mean to the actual mean of 57.7 degrees, we see that the computed mean is significantly lower. This suggests that the distribution is skewed to the left, with more low temperatures than high temperatures.