Final answer:
The median of the data set is 14, there is no mode, the mean is approximately 13.33, and the standard deviation requires a series of calculations. The range is 19.
Step-by-step explanation:
Calculating Median, Mode, Mean, Standard Deviation, and Range
To calculate the median of the data set 12, 26, 9, 16, 10, 7, first we need to arrange the numbers in ascending order:
9, 10, 12, 16, 26, 7. Since there is an even number of values, the median would be the average of the middle two values, which are 12 and 16. The median is therefore (12 + 16) / 2 = 14.
To compute the mode, we look for the number that appears most often in the data set. In this case, there are no repeating numbers, so the data set has no mode.
To calculate the mean (average), add all the numbers together and divide by the quantity of numbers. (9 + 10 + 12 + 16 + 26 + 7) / 6 = 13.33.
The standard deviation is a measure of the amount of variation or dispersion in a set of values. To calculate standard deviation, we need to follow a series of steps including finding the mean, the variance, and then taking the square root of the variance. Due to the complexity, we would typically use a calculator or statistical software for accurate computation.
The range of the data is the difference between the highest and lowest values, which is 26 - 7 = 19.