Question

The following stem-and-leaf plot represents the prices in dollars of general admission tickets for the last 1818 concerts at one venue. Use the data provided to find the quartiles.

Ticket Prices in Dollars

Stem   Leaves              
4   2   7   9   9          
5   1   3   4   9          
6   2   3   6              
7   0   1   2   3   5   7   7

Answer 1

First, we need to convert the data in plain form from stem and leaf plot

42 47 49 49 51 53 54 59 62 63 66 70 71 72 73 75 77 77

We have a total of 18 data points, i.e. even number of data sets.

Median or second quartile is halfway between the two middle data values for even number of observations

Two middle data values are 62 and 63

So, median or second quartile = (62+63)/2 = 62.5

Now, we need to divide the data set into two equal parts

lower half = 42 47 49 49 51 53 54 59 62 and upper half = 63 66 70 71 72 73 75 77 77

Now, we have odd data values in lower half and upper half

First quartile = middle value or center value for odd number of data values in lower half

middle value is 51

So, first quartile = 51

Similarly,

Third quartile = middle value or center value for odd number of data values in upper half

middle value is 72

So, third quartile = 72

Therefore

First quartile = 51

Second quartile or median = 62.5

Third quartile = 72