Answer:
Explanation:
The median is the middle value of the data set when it is arranged in order. Since we have grouped data, we can find the median by calculating the cumulative frequencies and identifying the interval that contains the median.
To find the cumulative frequencies, we add up the frequencies starting from the first class interval. We also need to calculate the total frequency:
class
Edition
0-100 100-200 200-300 300-400 400-500 500-600 600-700
15
17
f
12
9
5
2
Cumulative frequency
15
32
f + 32
f + 44
f + 53
f + 58
f + 60
Total frequency = 120
Since the median is 240, it falls within the third class interval (200-300). The cumulative frequency of the second class interval (100-200) is 15, and the cumulative frequency of the third class interval (200-300) is 32. So, the median corresponds to the 32nd observation.
We can now use the formula for the median of grouped data to find f:
Median = L + ((n/2 - CF) / f) * w
where:
L = lower limit of the class interval containing the median (200)
n = total frequency (120)
CF = cumulative frequency up to the interval containing the median (32)
f = frequency of the interval containing the median (unknown)
w = width of the class interval containing the median (100)
Substituting the known values, we get:
240 = 200 + ((60 - 32) / f) * 100
Simplifying and solving for f, we get:
f = (28 * 100) / 8
f = 350
Therefore, the missing frequency is 350.