Consider the following partially completed frequency table:
Class xi fi
[87; 97) 92 3
[97; 107) 102 5
[107; 117) 112 9
[117; 127) 122 11
[127; 137) 132 2
Determine the first quartile by using the appropriate formula.
130
106
140
116
To determine the first quartile, we need to find the position of the first quartile within the data set. The formula to find the position of the first quartile is:
Position of Q1 = (n+1)/4
Where n is the total number of data points. In this case, n is the sum of the frequencies: 3 + 5 + 9 + 11 + 2 = 30.
Therefore, the position of Q1 = (30+1)/4 = 31/4 = 7.75
Since the position of Q1 is not a whole number, we need to find the two data points in positions 7 and 8, which correspond to the value of the x axis at position 7.75.
The value of the x axis at position 7 corresponds to the [107; 117) class, which has an x value of 112. The value of the x axis at position 8 corresponds to the [117; 127) class, which has an x value of 122.
Therefore, the first quartile is 112.