Advertisements
Advertisements
Question
Calculate the missing frequency from the following distribution, it being given that the median of distribution is 24.
| Class | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 - 50 |
| Frequency | 5 | 25 | ? | 18 | 7 |
Solution
| Class | Frequency (fi) | Cumulative Frequency (cf) |
| 0 – 10 | 5 | 5 |
| 10 – 20 | 25 | 30 |
| 20 – 30 | x | x+30 |
| 30 – 40 | 18 | x+48 |
| 40 – 50 | 7 | x+55 |
Median is 24 which lies in 20 – 30
∴ Median class = 20 – 30
Let the unknown frequency be x.
Here, l = 20, `n/2 = (x+55)/2`, c.f. of the preceding class = c.f = 30, f = x, h = 10
Now,
Median, `M = l + (n/2−cf)/f× h`
`⇒ 24 = 20 + (x+55/2 − 30)/x × 10`
`⇒ 24 = 20 + (x + 55 − 60/2)/ x × 10`
⇒ 24 = 20 +` (x−5 )/(2x) `× 10
⇒ 24 = 20 + `(5x−25)/ x`
⇒ 24 = 20+`( 5x−25)/ x`
⇒ 24x = 25x – 25
⇒ –x = – 25
⇒ x = 25
Hence, the unknown frequency is 25.
APPEARS IN
RELATED QUESTIONS
Find the missing frequencies and the median for the following distribution if the mean is 1.46.
| No. of accidents: | 0 | 1 | 2 | 3 | 4 | 5 | Total |
| Frequency (No. of days): | 46 | ? | ? | 25 | 10 | 5 | 200 |
Find the median wages for the following frequency distribution:
| Wages per day (in Rs) | 61 – 70 | 71 – 80 | 81 – 90 | 91 – 100 | 101 – 110 | 111 – 120 |
| No. of women workers | 5 | 15 | 20 | 30 | 20 | 8 |
What is the value of the median of the data using the graph in the following figure of less than ogive and more than ogive?
If the mean of the following distribution is 3, find the value of p.
| x | 1 | 2 | 3 | 5 | p + 4 |
| f | 9 | 6 | 9 | 3 | 6 |
Find a certain frequency distribution, the value of mean and mode are 54.6 and 54 respectively. Find the value of median.
Find the median of the scores 7, 10, 5, 8, 9.
The median of the following observations 11, 12, 14, (x – 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of x and hence find the mean.
Find the median of the following distribution:
| Marks | 0 – 10 | 10 –20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 |
| Number of students | 5 | 8 | 20 | 15 | 7 | 5 |
Find the median of the following frequency distribution:
| Class: | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 | 80 – 100 |
| Frequency: | 6 | 8 | 5 | 9 | 7 |
The median of 100 observations grouped in classes of equal width is 25. If the median class interval is 20 –30 and the number of observations less than 20 is 45, then the frequency of median class is ______.
