A family of bears is going to a movie. The following data points represent the ticket and candy price (in dollars) for each bear. Find the interquartile range (IQR) of the data set.0, 1 1/2, 2 1/2, 3, 4, 4, 4, 7, 7 1/2
Accepted Solution
A:
Answer:The interquartile range (IQR) of the data set is: 3.5Step-by-step explanation:The data points are given as follows: 0, 1 1/2, 2 1/2, 3, 4, 4, 4, 7, 7 1/2i.e. 0 , 1.5 , 2.5 , 3 , 4 , 4 , 4 , 7 , 7.5There are a total of 9 data points and we know that the median of the data is the central tendency of the data and it always exist in the middle of the data.Here we have 9 data points.and hence the median exist at the the 5th place.Hence, Median of data of Middle quartile i.e. [tex]Q_2[/tex]= 4Also, the lower set of data is: 0 , 1.5 , 2.5 , 3and the first quartile or the lower quartile i.e. [tex]Q_1[/tex] is the median of the lower set of data.i.e. [tex]Q_1=\dfrac{1.5+2.5}{2}\\\\i.e.\\\\Q_1=2[/tex]The upper set of data is: 4 , 4 , 7 , 7.5and the third quartile or the upper quartile i.e. [tex]Q_3[/tex] is the median of the upper set of data.i.e. [tex]Q_3=\dfrac{4+7}{2}\\\\i.e.\\\\Q_3=5.5[/tex]Hence, the interquartile range (IQR) of the data set is given by:[tex]IQR=Q_3-Q_1\\\\i.e.\\\\IQR=5.5-2\\\\i.e.\\\\IQR=3.5[/tex]