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प्रश्न
The median of the following data is 50. Find the values of p and q, if the sum of all the frequencies is 90.
| Marks: | 20 -30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 |
| Frequency: | P | 15 | 25 | 20 | q | 8 | 10 |
The median of the following data is 50. Find the values of ‘p’ and ‘q’, if the sum of all frequencies is 90. Also find the mode of the data.
| Marks obtained | Number of students |
| 20 – 30 | p |
| 30 – 40 | 15 |
| 40 – 50 | 25 |
| 50 – 60 | 20 |
| 60 – 70 | q |
| 70 – 80 | 8 |
| 80 – 90 | 10 |
उत्तर
The given series is in inclusive form. Converting it to exclusive form and preparing the cumulative frequency table, we have
| Class interval | Frequency (fi ) | Cumulative Frequency (c.f.) |
| 20 – 30 | p | p |
| 30 – 40 | 15 | p + 15 |
| 40 – 50 | 25 | p + 40 |
| 50 – 60 | 20 | p + 60 |
| 60 – 70 | q | p + q + 60 |
| 70 – 80 | 8 | p + q + 68 |
| 80 – 90 | 10 | p + q + 78 |
| 78 + p + q = 90 |
Median = 50It lies in the interval 50 – 60, so the median class is 50 – 60.
Now, we have
l = 50, h = 10, f = 20, F = p + 40, N = 90
We know that
Median = `"l" + {("N"/2 - "f")/"f"} xx "h"`
`50 = 50 + (45 - ("p" + 40))/20xx10`
⇒ 0 = `(5 - "p")/2`
⇒ p = 5
And,
p + q + 78 = 90
⇒ p + q = 12
⇒ q = 12 - 5 = 7
Model = `"l" + ("f"_1 - "f"_0)/(2"f"_1 - "f"_0 - "f"_2)."h"`
= `40 + (25 - 15)/(2(25) - 15 - 20)xx10`
= `40 + 100/15`
= 40 + 6.67
= 46.67
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.
The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observations in the data:
| Class interval | Frequency |
| 0 - 100 | 2 |
| 100 - 200 | 5 |
| 200 - 300 | f1 |
| 300 - 400 | 12 |
| 400 - 500 | 17 |
| 500 - 600 | 20 |
| 600 - 700 | f2 |
| 700 - 800 | 9 |
| 800 - 900 | 7 |
| 900 - 1000 | 4 |
The median of the following data is 16. Find the missing frequencies a and b if the total of frequencies is 70.
| Class | 0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 |
| Frequency | 12 | a | 12 | 15 | b | 6 | 6 | 4 |
Calculate the median for the following data:
| Class | 19 – 25 | 26 – 32 | 33 – 39 | 40 – 46 | 47 – 53 | 54 - 60 |
| Frequency | 35 | 96 | 68 | 102 | 35 | 4 |
Find the median from the following data:
| Class | 1 – 5 | 6 – 10 | 11 – 15 | 16 – 20 | 21 – 25 | 26 – 30 | 31 – 35 | 35 – 40 | 40 – 45 |
| Frequency | 7 | 10 | 16 | 32 | 24 | 16 | 11 | 5 | 2 |
A data has 25 observations arranged in a descending order. Which observation represents the median?
In the graphical representation of a frequency distribution, if the distance between mode and mean is ktimes the distance between median and mean, then write the value of k.
The abscissa of the point of intersection of less than type and of the more than types cumulative frequency curves of a grouped data gives its ______.
Will the median class and modal class of grouped data always be different? Justify your answer.
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.
