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Answer: Median for frequency distribution
To calculate the median for this frequency distribution, you will need to follow these steps:
- Find the total frequency by adding up all the frequencies in the table. In this case, the total frequency is 977.
- Determine the midpoint of the frequency distribution for each age group. To do this, add the lower and upper limits of each age group and divide by 2. For example, the midpoint for the age group 15-20 is (15+20)/2 = 17.5.
- Calculate the cumulative frequency for each age group by adding up the frequencies from the first age group to the current age group. For example, the cumulative frequency for the age group 20-25 is 59+197 = 256.
- Identify the median age group. This is the age group that contains the middle value of the distribution. To find this, divide the total frequency by 2 to get 488.5. Then, find the age group that contains this value in the cumulative frequency column. In this case, it is the age group 25-30.
- Calculate the median age. To do this, use the formula:
Median = L + ((N/2 - CF)/f) x w
Whe
L = lower limit of the median age group (25)
N = total frequency (977)
CF = cumulative frequency of the age group before the median age group (256)
f = frequency of the median age group (263)
w = width of the age group (5)
Plugging in the values, we get:
Median = 25 + ((488.5 - 256)/263) x 5
Median = 27.5
Therefore, the median age for this frequency distribution is 27.5.
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