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प्रश्न
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 |
उत्तर
We prepare the cumulative frequency table, as shown below:
| Age (in years) | Number of patients `(f_i)` | Cumulative Frequency (cf) |
| 0 – 15 | 5 | 5 |
| 15 – 30 | 20 | 25 |
| 30 – 45 | 40 | 65 |
| 45 – 60 | 50 | 115 |
| 60 – 75 | 25 | 140 |
| Total | `N = Σ f_i` = 140 |
Now, N = 140 ⇒`N/2 = 70`
The cumulative frequency just greater than 70 is 115 and the corresponding class is 45 –60
Thus, the median class is 45 – 60.
∴ l = 45, h = 15, f = 50, N = 140 and cf = 65.
Now,
Median = l + `((N/2-cf)/f) xx h`
=`45 + ((140/2-65)/50) xx 15`
=`45+((70-65)/50) xx 15`
= 45 + 1.5
= 46.5
Hence, the median age is 46.5 years.
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संबंधित प्रश्न
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.
For a certain frequency distribution, the value of mean is 20 and mode is 11. Find the value of median.
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| I.Q.: | 55 - 64 | 65 - 74 | 75 - 84 | 85 - 94 | 95 - 104 | 105 - 114 | 115 - 124 | 125 - 134 | 135 - 144 |
| No of Students: | 1 | 2 | 9 | 22 | 33 | 22 | 8 | 2 | 1 |
From the following data, find:
Median
25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38 and 83
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| Class | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 - 50 |
| Frequency | 5 | 25 | ? | 18 | 7 |
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| Rainfall (in cm ): | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Number of days : | 22 | 10 | 8 | 15 | 5 | 6 |
Calculate the median rainfall using ogives of more than type and less than type.
Write the median class of the following distribution:
| Class-interval: | 0−10 | 10−20 | 20−30 | 30−40 | 40−50 | 50−60 | 60−70 |
| Frequency: | 4 | 4 | 8 | 10 | 12 | 8 | 4 |
In a hospital, weights of new born babies were recorded, for one month. Data is as shown:
| Weight of new born baby (in kg) | 1.4 - 1.8 | 1.8 - 2.2 | 2.2 - 2.6 | 2.6 - 3.0 |
| No of babies | 3 | 15 | 6 | 1 |
Then the median weight is?
Heights of 50 students of class X of a school are recorded and following data is obtained:
| Height (in cm) | 130 – 135 | 135 – 140 | 140 – 145 | 145 – 150 | 150 – 155 | 155 – 160 |
| Number of students | 4 | 11 | 12 | 7 | 10 | 6 |
Find the median height of the students.
