Advertisements
Advertisements
Question
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 |
Solution
| Marks | No. of students (f) |
c.f. |
| 0 – 10 | 5 | 5 |
| 10 – 20 | 8 | 13 |
| 20 – 30 | 20 | 33 |
| 30 – 40 | 15 | 48 |
| 40 – 50 | 7 | 55 |
| 50 – 60 | 5 | 60 |
| `sum"f"` = 60 |
Here, N = `sum"f"` = 60
∴ `"N"/2 = 60/2` = 30
So, the median class is 20 – 30
Lower limit of median class, l = 20
Class size, h = 10
Cumulative frequency of preceding class, c.f. = 13
Frequency of median class, f = 20
∴ Median = `"l" + (("N" / 2 - "c.f."))/"f" xx "h"`
= `20 + ((60 /2 - 13)/20) xx 10`
= `20 + 17/2`
= 20 + 8.5
= 28.5
APPEARS IN
RELATED QUESTIONS
The following table shows ages of 3000 patients getting medical treatment in a hospital on a particular day :
| Age (in years) | No. of Patients |
| 10-20 | 60 |
| 20-30 | 42 |
| 30-40 | 55 |
| 40-50 | 70 |
| 50-60 | 53 |
| 60-70 | 20 |
Find the median age of the patients.
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
| Weight (in kg) | 40−45 | 45−50 | 50−55 | 55−60 | 60−65 | 65−70 | 70−75 |
| Number of students | 2 | 3 | 8 | 6 | 6 | 3 | 2 |
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 |
From the following data, find:
Median
25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38 and 83
In a hospital, the ages of diabetic patients were recorded as follows. Find the median age.
| Age (in years) |
0 – 15 | 15 – 30 | 30 – 45 | 45 – 60 | 60 - 75 |
| No. of patients | 5 | 20 | 40 | 50 | 25 |
The following table shows the daily wages of workers in a factory:
| Daily wages in (Rs) | 0 – 100 | 100 – 200 | 200 – 300 | 300 – 400 | 400 – 500 |
| Number of workers | 40 | 32 | 48 | 22 | 8 |
Find the median daily wage income of the workers.
The following frequency distribution table shows the number of mango trees in a grove and their yield of mangoes, and also the cumulative frequencies. Find the median of the data.
| Class (No. of mangoes) |
Frequency (No. of trees) |
Cumulative frequency (less than) |
| 50-100 | 33 | 33 |
| 100-150 | 30 | 63 |
| 150-200 | 90 | 153 |
| 200-250 | 80 | 233 |
| 250-300 | 17 | 250 |
If the median of the data: 24, 25, 26, x + 2, x + 3, 30, 31, 34 is 27.5, then x =
The arithmetic mean and mode of a data are 24 and 12 respectively, then its median is
The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching centre are given as follows:
| Speed (km/h) | 85 – 100 | 100 – 115 | 115 – 130 | 130 – 145 |
| Number of players | 11 | 9 | 8 | 5 |
Calculate the median bowling speed.
