Final answer:
The range of the data is 15. The interquartile range is 8.5. The variance is approximately 8.484375 and the standard deviation is approximately 2.913.
Step-by-step explanation:
A) To find the range of a set of data, subtract the lowest value from the highest value. For the given data set, the lowest value is 18 and the highest value is 33, so the range is 33 - 18 = 15.
B) To find the interquartile range, first find the first quartile (Q1) and the third quartile (Q3). The first quartile is the median of the lower half of the data set, which consists of 18, 22, 25, and 25. In ascending order, these values are 18, 22, 25, 25, so the median is the average of the middle two values, which is (22 + 25) / 2 = 23.5. The third quartile is the median of the upper half of the data set, which consists of 29, 31, 33, and 33. In ascending order, these values are 29, 31, 33, 33, so the median is the average of the middle two values, which is (31 + 33) / 2 = 32. The interquartile range is Q3 - Q1 = 32 - 23.5 = 8.5.
C) To find the variance, first find the mean of the data set. The mean is the sum of all the values divided by the number of values. The sum of the data values is 26 + 25 + 22 + 18 + 31 + 33 + 29 + 25 = 209, and there are 8 values, so the mean is 209 / 8 = 26.125. Then, subtract the mean from each data value, square the result, and add up all the squared differences. Divide the sum of the squared differences by the number of values to find the variance. In this case, the sum of the squared differences is (26 - 26.125)^2 + (25 - 26.125)^2 + (22 - 26.125)^2 + (18 - 26.125)^2 + (31 - 26.125)^2 + (33 - 26.125)^2 + (29 - 26.125)^2 + (25 - 26.125)^2 = 67.875, and there are 8 values, so the variance is 67.875 / 8 = 8.484375.
D) To find the standard deviation, take the square root of the variance. In this case, the square root of 8.484375 is approximately 2.913.