Final answer:
The mean of the given data is 10, and the mode is 12. A step-by-step explanation was provided for finding the mean, standard deviation, and mode of a set of values. The standard deviation calculation involves squaring the differences from the mean, taking the average of those squares, and then taking the square root.
Step-by-step explanation:
Finding Mean, Standard Deviation, and Mode
To find the mean of the numbers [12,3,16,12,6,7,9,14,12,11,8], you need to add all the numbers together and then divide by the total number of values. The mean (average) is calculated as follows:
(12 + 3 + 16 + 12 + 6 + 7 + 9 + 14 + 12 + 11 + 8) / 11 = 110 / 11 = 10.
The mean number of text messages received is 10.
Calculating the standard deviation involves several steps. First, you find the mean. Then, subtract the mean from each value, square the result, and find the mean of those squared differences. Finally, take the square root of this last mean to get the standard deviation.
To find the mode, look for the number that appears most often in the list. In this case, the number 12 appears three times, which is more than any other number, making it the mode.