How do I figure out how to do b,c,d?
The box and whisker plot shows the number of text messages received in one day by students in seventh and eighth grade at Lincoln Middle School.
a) Describe the overlap of the two sets of data.
b) Find the IQR of each set.
c) Find the difference between the medians of the sets.
d) What number multiplied by the IQR equals the difference between the medians of the two sets?
To figure out how to solve parts b, c, and d, you will need to understand some key concepts related to box and whisker plots and measures of central tendency. Here's how you can approach each part of the problem:
a) To describe the overlap of the two sets of data shown in the box and whisker plot, start by examining the position of the boxes and whiskers for each set. Look for any overlaps or intersections between the two boxes or whiskers. If the boxes overlap, it indicates that there is a range of values common to both sets of data. If the whiskers overlap, it suggests that there are some outlier values present in both sets. Describe these observations in words.
b) To find the Interquartile Range (IQR) of each set of data, you need to calculate the difference between the third quartile (Q3) and the first quartile (Q1). The third quartile represents the value below which 75% of the data lies, while the first quartile represents the value below which 25% of the data lies. Subtracting Q1 from Q3 gives you the IQR, which represents the range of the middle 50% of the data. Calculate the IQR separately for each set of data shown in the box and whisker plot.
c) To find the difference between the medians of the two sets, identify the median for each set of data. The median is the middle value when the data is arranged in increasing order. Simply subtract the median of one set from the median of the other set to find the difference.
d) Finally, to determine the number that, when multiplied by the IQR, equals the difference between the medians of the two sets, divide the difference between the medians by the IQR of either set. This will give you the value you are looking for.
Make sure to extract the necessary data from the box and whisker plot accurately, and perform the calculations step by step to get the answers to parts b, c, and d.