Final answer:
The calculations for the dataset (135, 126, 107, 80, 125, 133, 141, 148) show a mean of 124.375, a median of 129.5, no mode, a first quartile (Q1) of 116, a third quartile (Q3) of 138, an interquartile range (IQR) of 22, and a range of 68.
Step-by-step explanation:
To calculate the mean, add all the data points together and divide by their number. The dataset provided is: 135, 126, 107, 80, 125, 133, 141, 148. Adding these gives a sum of 995, and since there are 8 data points, the mean is 995 ÷ 8 = 124.375.
To find the median, sort the data and locate the middle point. The sorted dataset is: 80, 107, 125, 126, 133, 135, 141, 148. With 8 numbers, the median will be the average of the 4th and 5th numbers, which are 126 and 133, so the median is (126 + 133) ÷ 2 = 129.5.
The mode is the most frequently occurring data point. In this set, there is no number that occurs more than once, so the dataset has no mode.
The first quartile (Q1) is the median of the lower half, excluding the median if the dataset has an odd number of data points. For our even set of 8, Q1 is the median of the first 4 numbers, which means it is the average of 107 and 125. So, Q1 = (107 + 125) ÷ 2 = 116.
The third quartile (Q3) is similarly the median of the upper half. Here it is the average of 135 and 141, so Q3 = (135 + 141) ÷ 2 = 138.
The interquartile range (IQR) is the difference between Q3 and Q1. So, IQR = 138 - 116 = 22.
Lastly, the range is the difference between the highest and lowest value. Range = 148 - 80 = 68.