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Sagot :
Step-by-step explanation:
To find the median of a frequency distribution with range values, you can use the following steps:
1. Determine the cumulative frequency distribution by adding the frequencies of each interval.
2. Identify the total number of data points (N) by summing the frequencies.
3. Calculate the median class interval by finding the interval that contains the middle value (N/2).
4. Use the following formula to estimate the median:
Median = L + [(N/2 - CF)/f] x w
Where:
- L = Lower boundary of the median class interval
- CF = Cumulative frequency up to the median class interval
- f = Frequency of the median class interval
- w = Width of the median class interval
Note: This method assumes a continuous distribution and uses interpolation to estimate the median.
Example:
Interval Frequency
0-9 5
10-19 8
20-29 12
30-39 7
40-49 3
Cumulative Frequency:
0-9 5
10-19 13 (5+8)
20-29 25 (13+12)
30-39 32 (25+7)
40-49 35 (32+3)
Total data points (N) = 35
Median class interval = 20-29 (contains the middle value 35/2 = 17.5)
Median = 20 + [(17.5 - 13)/12] x 10 = 23.75
So, the estimated median is 23.75.
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