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प्रश्न
Find the unknown entries a, b, c, d, e, f in the following distribution of heights of students in a class:
| Height (in cm) |
Frequency | Cumulative frequency |
| 150 – 155 | 12 | a |
| 155 – 160 | b | 25 |
| 160 – 165 | 10 | c |
| 165 – 170 | d | 43 |
| 170 – 175 | e | 48 |
| 175 – 180 | 2 | f |
| Total | 50 |
उत्तर
| Height (in cm) |
Frequency | Cumulative frequency (given) |
Cumulative frequency |
| 150 – 155 | 12 | a | 12 |
| 155 – 160 | b | 25 | 12 + b |
| 160 – 165 | 10 | c | 22 + b |
| 165 – 170 | d | 43 | 22 + b + d |
| 170 – 175 | e | 48 | 22 + b + d + e |
| 175 – 180 | 2 | f | 24 + b + d + e |
| Total | 50 |
On comparing last two tables, we get
a = 12
∴ 12 + b = 25
⇒ b = 25 – 12 = 13
22 + b = c
⇒ c = 22 + 13 = 35
22 + b + d = 43
⇒ 22 + 13 + d = 43
⇒ d = 43 – 35 = 8
And 22 + b + d + e = 48
⇒ 22 + 13 + 8 + e = 48
⇒ e = 48 – 43 = 5
And 24 + b + d + e = f
⇒ 24 + 13 + 8 + 5 = f
∴ f = 50
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संबंधित प्रश्न
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| Monthly Consumption (in units) | 140 – 160 | 160 – 180 | 180 – 200 | 200 – 220 | 220 – 240 | 240 – 260 | 260 - 280 |
| Number of Families | 3 | 8 | 15 | 40 | 50 | 30 | 10 |
Prepare a ‘more than type’ ogive for the given frequency distribution.
From the following frequency, prepare the ‘more than’ ogive.
| Score | Number of candidates |
| 400 – 450 | 20 |
| 450 – 500 | 35 |
| 500 – 550 | 40 |
| 550 – 600 | 32 |
| 600 – 650 | 24 |
| 650 – 700 | 27 |
| 700 – 750 | 18 |
| 750 – 800 | 34 |
| Total | 230 |
Also, find the median.
What is the cumulative frequency of the modal class of the following distribution?
| Class | 3 – 6 | 6 – 9 | 9 – 12 | 12 – 15 | 15 – 18 | 18 – 21 | 21 – 24 |
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7 | 13 | 10 | 23 | 54 | 21 | 16 |
The following table, construct the frequency distribution of the percentage of marks obtained by 2300 students in a competitive examination.
| Marks obtained (in percent) | 11 – 20 | 21 – 30 | 31 – 40 | 41 – 50 | 51 – 60 | 61 – 70 | 71 – 80 |
| Number of Students | 141 | 221 | 439 | 529 | 495 | 322 | 153 |
(a) Convert the given frequency distribution into the continuous form.
(b) Find the median class and write its class mark.
(c) Find the modal class and write its cumulative frequency.
Write the modal class for the following frequency distribution:
| Class-interval: | 10−15 | 15−20 | 20−25 | 25−30 | 30−35 | 35−40 |
| Frequency: | 30 | 35 | 75 | 40 | 30 | 15 |
If \[u_i = \frac{x_i - 25}{10}, \Sigma f_i u_i = 20, \Sigma f_i = 100, \text { then }\]`overlineX`
The arithmetic mean of the following frequency distribution is 53. Find the value of k.
| Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| Frequency | 12 | 15 | 32 | k | 13 |
Calculate the mean of the following frequency distribution :
| Class: | 10-30 | 30-50 | 50-70 | 70-90 | 90-110 | 110-130 |
| Frequency: | 5 | 8 | 12 | 20 | 3 | 2 |
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| Class interval: | 20−30 | 30−40 | 40−50 | 50−60 | 60−70 | 70−80 | 80−90 |
| Frequency: | 10 | 8 | 12 | 24 | 6 | 25 | 15 |
Consider the following distribution:
| Marks obtained | Number of students |
| More than or equal to 0 | 63 |
| More than or equal to 10 | 58 |
| More than or equal to 20 | 55 |
| More than or equal to 30 | 51 |
| More than or equal to 40 | 48 |
| More than or equal to 50 | 42 |
The frequency of the class 30 – 40 is:
