Advertisements
Advertisements
प्रश्न
An incomplete distribution is given as follows:
| Variable: | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |
| Frequency: | 10 | 20 | ? | 40 | ? | 25 | 15 |
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.
उत्तर
| Class interval | Frequency | Cumulative frequency |
| 0 - 10 | 10 | 10 |
| 10 - 20 | 20 | 30 |
| 20 - 30 | f1 | 30 + f1 |
| 30 - 40 | 40 | 70 + f1 |
| 40 - 50 | f2 | 70 + f1 + f2 |
| 50 - 60 | 25 | 95 + f1 + f2 |
| 60 - 70 | 15 | 110 + f1 + f2 |
| N = 170 |
Given median = 35
The median class = 30 - 40
l = 30, h = 40 - 30 = 10, f = 40, F = 30 + f1
Median `=l+{(N/2-F)/f}xxh`
`35=30+{(85-(30 + f1))/40}xx10`
`35=30+(55-f1)/40xx10`
`35-30=(55-f1)/4`
`5=(55-f1)/4`
5 x 4 = 55 - f1
20 = 55 - f1
f1 = 55 - 20
f1 = 35
Given
Sum of frequencies = 170
⇒ 10 + 20 + f1 + 40 + f2 + 25+ 15 = 170
⇒ 10 + 20 + 35 + 40 + f2 + 25+ 15 = 170
⇒ 145 + f2 = 170
⇒ f2 = 170 - 145
⇒ f2 = 25
∴ f1 = 35 and f2 = 25
APPEARS IN
संबंधित प्रश्न
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:
| Number of letters | Number of surnames |
| 1 - 4 | 6 |
| 4 − 7 | 30 |
| 7 - 10 | 40 |
| 10 - 13 | 6 |
| 13 - 16 | 4 |
| 16 − 19 | 4 |
Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.
Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:
715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719.
The marks obtained by 19 students of a class are given below:
27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35 and 28.
Find:
- Median
- Lower quartile
- Upper quartile
- Inter-quartile range
From the following data, find:
Inter-quartile range
25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38 and 83
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 |
A data has 25 observations arranged in a descending order. Which observation represents the median?
The annual rainfall record of a city for 66 days is given in the following table :
| 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.
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?
Find the median of the scores 7, 10, 5, 8, 9.
Obtain the median for the following frequency distribution:
| x : | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| f : | 8 | 10 | 11 | 16 | 20 | 25 | 15 | 9 | 6 |
