The box-and-whisker plot below shows the numbers of text messages received in one day by students in the seventh and eighth grades 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?
Without being able to see your image, here are some guidelines:
a) Consider how the key pieces of data on one graph compare to those on the other graph (e.g. compare the mins, lower quartiles, medians, upper quartiles, and maxes).
b) IQR = Q3 - Q1 (ends of the box)
c) Find the difference between the Q2s of each set. (line in centre of each box)
d) Use the numbers you found above to work this out.
a) To describe the overlap of the two sets of data, we examine the box-and-whisker plot. The boxplot shows two boxes, one for each set of data (seventh grade and eighth grade). There is overlap between the two boxes, meaning that there are values in the data sets that are common to both grades.
b) To find the Interquartile Range (IQR) of each set, we need to locate the first quartile (Q1) and the third quartile (Q3) for each set. The IQR is then calculated as Q3 - Q1.
c) To find the difference between the medians of the two sets, we subtract the median of one set from the median of the other set.
d) To find the number that, when multiplied by the IQR, equals the difference between the medians of the two sets, we divide the difference between the medians by the IQR.
To answer these questions, we need to interpret the given box-and-whisker plot and find the required values. Let's break it down step by step:
a) Describe the overlap of the two sets of data:
Looking at the box-and-whisker plot, we can compare the positions of the boxes, whiskers, and medians to understand the overlap. If the boxes overlap, it means there is some common data between the two sets. If the whiskers overlap, it indicates that the range of values in both sets overlaps.
b) Find the IQR of each set:
The Interquartile Range (IQR) is a measure of statistical dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3). To find the IQR for each set, locate the lower (Q1) and upper (Q3) quartiles in the box-and-whisker plot and subtract Q1 from Q3 for each set.
c) Find the difference between the medians of the sets:
The median is the middle value of a dataset. To find the difference between the medians of the two sets, subtract the median of one set from the median of the other.
d) What number multiplied by the IQR equals the difference between the medians of the two sets:
To find this number, we need to divide the difference between the medians of the two sets by the IQR of either set.
Please provide a clear image or description of the box-and-whisker plot for a more detailed explanation and to find the numerical values necessary to calculate the answers.