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.
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
1 answer
1 answer