Answer :
Answer:
To find the median from the given frequency distribution, follow these steps:
1. **Identify the Median Class**:
- The median is the value that separates the higher half from the lower half of the data set.
- First, find the total number of observations (N). This is the cumulative frequency (cf) of the last class.
- Here, \( N = 49 \).
2. **Locate the Median Position**:
- The median position can be found using the formula \( \frac{N}{2} \).
- So, the median position is \( \frac{49}{2} = 24.5 \).
3. **Determine the Median Class**:
- The median class is the class interval where the cumulative frequency just exceeds or contains the median position (24.5).
- From the cumulative frequencies given, the median class is 15-20, as its cumulative frequency is 26, which contains 24.5.
4. **Apply the Median Formula**:
- Use the formula for the median in a grouped frequency distribution:
\[
\text{Median} = L + \left(\frac{\frac{N}{2} - CF}{f}\right) \times h
\]
- Here:
- \( L \) is the lower boundary of the median class.
- \( CF \) is the cumulative frequency of the class before the median class.
- \( f \) is the frequency of the median class.
- \( h \) is the class width.
For the given data:
- \( L = 15 \) (lower boundary of the median class 15-20)
- \( CF = 11 \) (cumulative frequency of the class before the median class 10-15)
- \( f = 15 \) (frequency of the median class 15-20)
- \( h = 5 \) (class width)
Substitute these values into the formula:
\[
\text{Median} = 15 + \left(\frac{24.5 - 11}{15}\right) \times 5
\]
Simplify the expression inside the parentheses:
\[
\text{Median} = 15 + \left(\frac{13.5}{15}\right) \times 5
\]
\[
\text{Median} = 15 + \left(0.9\right) \times 5
\]
\[
\text{Median} = 15 + 4.5 = 19.5
\]
Thus, the median of the frequency distribution is **19.5**.
This method effectively provides the median for grouped data by identifying the median class and applying the appropriate formula [[❞]](https://quizgecko.com/learn/survey-of-india-map-sheet-g43s10-analytical-questions-effnfc).
Answer:
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Explanation:
Σfi= 49
N = Σfi = 49
⇒ N/2 = 24.5
The cumulative frequency greater than 24.5 is 26 and the corresponding class is 15-20.
Thus the median class is 15-20.
Therefore,
l= 15,
h = 5,
f= 15,
c.f. of preceding class = 11 and N/2 = 24.5
Median,
M = l + ((N/2 − cf)/f) × h
Median = 15 + ((24.5 – 11)/15) × 5
Median = 15 + 4.5
Median = 19.5
Hence, median is 19.5 .