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 median by using the appropriate formula.
125.535
120
114.78
135.654
To determine the median, we first need to find the total number of observations (N). This can be found by summing up all the frequencies (fi) in the frequency table.
N = 3 + 5 + 9 + 11 + 2
N = 30
The median is the middle value when all values are arranged in order. Since the data is grouped, we will need to use the following formula to find the median:
Median = L + ((N/2 - F)/f) * w
Where:
L = Lower boundary of the median group
N = Total number of observations
F = Cumulative frequency of the group before the median group
f = Frequency of the median group
w = Width of each class interval
In this case, the median group is [117; 127), with lower boundary L = 117, cumulative frequency F = 3+5+9 = 17, frequency f = 11, and width of each class interval w = 10.
Now we plug these values into the formula:
Median = 117 + ((30/2 - 17)/11) * 10
Median = 117 + ((15 - 17)/11) * 10
Median = 117 + (-2/11) * 10
Median = 117 - 1.82
Median ≈ 115.18
Therefore, the median is approximately 115.18.