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प्रश्न
Find the Median of the following distribution:
| x | 3 | 5 | 10 | 12 | 8 | 15 |
| f | 2 | 4 | 6 | 10 | 8 | 7 |
उत्तर
Arranging the terms in ascending order and preparing the cumulative frequency table:
| x | f | c.f. |
| 3 | 2 | 2 |
| 5 | 4 | 6 |
| 8 | 8 | 14 |
| 10 | 6 | 20 |
| 12 | 10 | 30 |
| 15 | 7 | 37 |
Here, n = 37 which is odd.
So Median = `(("n" + 1)/2)^"th" "term"`
= `((37 + 1)/2)^"th" "term"`
= `(38/2)^"th"`
= 19th term
Hence, Median is the value of the 9th term = 10.
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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.
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| Variable: | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| Frequency: | 12 | 30 | - | 65 | - | 25 | 18 |
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(i) Using the median formula fill up missing frequencies.
(ii) Calculate the AM of the completed distribution.
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| Marks | 0 – 7 | 7 – 14 | 14 – 21 | 21 – 28 | 28 – 35 | 35 – 42 | 42 – 49 |
| Number of Students | 3 | 4 | 7 | 11 | 0 | 16 | 9 |
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| Runs scored | 2500 – 3500 | 3500 – 4500 | 4500 – 5500 | 5500 – 6500 | 6500 – 7500 | 7500 - 8500 |
| Number of batsman | 5 | x | y | 12 | 6 | 2 |
The following frequency distribution table gives the ages of 200 patients treated in a hospital in a week. Find the mode of ages of the patients.
| Age (years) | Less than 5 | 5 - 9 | 10 - 14 | 15 - 19 | 20 - 24 | 25 - 29 |
| No. of patients | 38 | 32 | 50 | 36 | 24 | 20 |
If 35 is removed from the data, 30, 34, 35, 36, 37, 38, 39, 40 then the median increases by ______.
The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its ______.
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 |
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The median of the following frequency distribution is 25. Find the value of x.
| Class: | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency: | 6 | 9 | 10 | 8 | x |
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| Family size | 1 – 3 | 3 – 5 | 5 – 7 | 7 – 9 | 9 – 11 |
| Numbers of Families | 7 | 8 | 2 | 2 | 1 |
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