Answer:
a. The IQR = 75th percentile – 25th percentile or Q3 – Q1
b. Median for data set 1 – median for data set 2
c. Data is either positively skewed, negatively skewed or normally/ equally distributed. Median is usually better since its accuracy is not affected by outliers like the mean.
d. Unusual/ inconsistent sampling
Step-by-step explanation:
Since there is no data set (s) given, there cannot be actual calculations done to answer the questions. Only the explanations and formulas can be given.
a. The interquartile range (IQR) is given as the difference between the 75th percentile (Q3) and the 25th percentile (Q1). For example, Q3 is 50 and Q1 is 20, the IQR is 50 – 20 = 30.
b. Since there is no data set given, one cannot determine the median of each data set. The median is the middlemost value. The difference would be given by subtracting the median of one data set from the median of the other. For example, if the median for data set 1 is 15 and the median for data set is 13, the difference would be 15 – 13 and the answer is 2.
c. The median is best if the data has a positive (tail is on the right) or negative skew (tail is on the left). The mean is a better measure when the data is normally distributed or symmetrical (bell shaped) and there are no outliers. Outliers can overstate the or understate the mean.
d. There can be many reasons why there are outliers in a data set. Some of these are recording errors when the data was taken, unusual/ inconsistent sampling when the sample was taken, measurement errors and experimental errors in the data set.
