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प्रश्न
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 |
Calculate the median bowling speed.
उत्तर
First we construct the cumulative frequency table
| Speed (in km/h) |
Number of players |
Cumulative frequency |
| 85 – 100 | 11 | 11 |
| 100 – 115 | 9 | 11 + 9 = 20 |
| 115 – 130 | 8 | 20 + 8 = 28 |
| 130 – 145 | 5 | 28 + 5 = 33 |
It is given that, n = 33
∴ `n/2 = 33/2 = 16.5`
So, the median class is 100 – 115.
Where, lower limit (l) = 100,
Frequency (f) = 9,
Cumulative frequency (cf) = 11
And class width (h) = 15
∴ Median = `l + ((n /2 - cf))/f xx h`
= `100 + ((16.5 - 11))/9 xx 15`
= `100 + (5.5 xx 15)/9`
= `100 + 82.5/9`
= 100 + 9.17
= 109.17
Hence, the median bowling speed is 109.17 km/h.
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संबंधित प्रश्न
An incomplete distribution is given below:
| Variable: | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| Frequency: | 12 | 30 | - | 65 | - | 25 | 18 |
You are given that the median value is 46 and the total number of items is 230.
(i) Using the median formula fill up missing frequencies.
(ii) Calculate the AM of the completed distribution.
Compute the median for the following data:
| Marks | No. of students |
| More than 150 | 0 |
| More than 140 | 12 |
| More than 130 | 27 |
| More than 120 | 60 |
| More than 110 | 105 |
| More than 100 | 124 |
| More than 90 | 141 |
| More than 80 | 150 |
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 |
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 |
The following are the marks scored by the students in the Summative Assessment exam
| Class | 0 − 10 | 10 − 20 | 20 − 30 | 30 − 40 | 40 − 50 | 50 − 60 |
| No. of Students | 2 | 7 | 15 | 10 | 11 | 5 |
Calculate the median.
The median of set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set ______.
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.
The median of the following frequency distribution is 35. Find the value of x.
| Class: | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency: | 6 | 3 | x | 12 | 19 |
Read the following passage and answer the questions given below.
|
Electric buses are becoming popular nowadays. These buses have the electricity stored in a battery. Electric buses have a range of approximately 280 km with just charge. These buses are superior to diesel buses as they reduce brake wear and also reduce pollution. 'transport department of a city wants to buy some electric buses for the city. So, the department wants to know the distance travelled by existing public transport buses in a day. The following data shows the distance travelled by 50 existing public transport buses in a day.
|
| Daily distance travelled (in km) | 100 – 120 | 120 – 140 | 140 – 160 | 160 – 180 | 180 – 200 |
| Number of buses | 12 | 14 | 8 | 6 | 10 |
- Find the 'median' distance travelled by a bus.
- Find the 'mean (average)' distance travelled by a bus.
If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately ______.
