Answer :
Final answer:
Using the cumulative frequency method, we determine that the cumulative frequency up to the median is 125. To find the missing frequency, we compare the cumulative frequency at or below the median with half of the total frequency. Therefore, the correct answer is not provided among the options.
Explanation:
To find the missing frequency for the interval 50-60, given that the median is 46, we can use the cumulative frequency method.
First, let's calculate the cumulative frequencies:
Cumulative frequency for 20-30: 20
Cumulative frequency for 20-40: 20 + 40 = 60
Cumulative frequency for 20-50: 20 + 40 + 65 = 125
Since the median is 46, it falls within the 40-50 interval, which has a cumulative frequency of 125.
Now, we know that the cumulative frequency at or below the median should be half of the total frequency. So, we need to find the total frequency:
Total frequency = Sum of all frequencies = 20 + 40 + 65 + ? + 30 + 40 + 25 = 220 + ?
Since the cumulative frequency at or below the median is 125, we have:
125 + Missing frequency in the interval 50-60 > Total frequency / 2
Plugging in the known values:
125 + Missing frequency > (220 + Missing frequency) / 2
Now, let's solve for the missing frequency:
125 + Missing frequency > (220 + Missing frequency) / 2
Multiply both sides by 2 to eliminate the fraction:
250 + 2 * Missing frequency > 220 + Missing frequency
Subtract 220 from both sides:
30 + 2 * Missing frequency > Missing frequency
Subtract Missing frequency from both sides:
30 > -Missing frequency
Since the missing frequency must be positive, we can conclude that:
Missing frequency = 30
So, the missing frequency for the interval 50-60 is 30.
Therefore, the correct answer is not provided among the options.
