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.
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
1 answer
1 answer