Advertisements
Advertisements
Question
Find the median of the following frequency distribution:
| x | 10 | 11 | 12 | 13 | 14 | 15 |
| f | 1 | 4 | 7 | 5 | 9 | 3 |
Solution
| x | f | c.f. |
| 10 | 1 | 1 |
| 11 | 4 | 5 |
| 12 | 7 | 12 |
| 13 | 5 | 17 |
| 14 | 9 | 26 |
| 15 | 3 | 29 |
n = 29 (odd)
∴ Median = `(("n" + 1)/2)^"th" "value"`
= `((29 + 1)/2)^"th" "value"`
= 15th value
= 13.
APPEARS IN
RELATED QUESTIONS
Below is the given frequency distribution of words in an essay
| Number of Words | Number of Candidates |
| 600 – 800 | 8 |
| 800 – 1000 | 22 |
| 1000 – 1200 | 40 |
| 1200 – 1400 | 18 |
| 1400 - 1600 | 12 |
Find the mean number of words written.
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.
In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000. Find the missing frequencies x and y.
| Runs scored | 2500 – 3500 | 3500 – 4500 | 4500 – 5500 | 5500 – 6500 | 6500 – 7500 | 7500 - 8500 |
| Number of batsman | 5 | x | y | 12 | 6 | 2 |
Find the median wages for the following frequency distribution:
| Wages per day (in Rs) | 61 – 70 | 71 – 80 | 81 – 90 | 91 – 100 | 101 – 110 | 111 – 120 |
| No. of women workers | 5 | 15 | 20 | 30 | 20 | 8 |
The following frequency distribution table shows the number of mango trees in a grove and their yield of mangoes, and also the cumulative frequencies. Find the median of the data.
| Class (No. of mangoes) |
Frequency (No. of trees) |
Cumulative frequency (less than) |
| 50-100 | 33 | 33 |
| 100-150 | 30 | 63 |
| 150-200 | 90 | 153 |
| 200-250 | 80 | 233 |
| 250-300 | 17 | 250 |
If 35 is removed from the data: 30, 34, 35, 36, 37, 38, 39, 40, then the median increased by
Consider the following frequency distribution:
| Class | 0 – 5 | 6 – 11 | 12 – 17 | 18 – 23 | 24 – 29 |
| Frequency | 13 | 10 | 15 | 8 | 11 |
The upper limit of the median class is:
Will the median class and modal class of grouped data always be different? Justify your answer.
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.
The monthly expenditure on milk in 200 families of a Housing Society is given below:
| Monthly Expenditure (in ₹) |
1000 – 1500 | 1500 – 2000 | 2000 – 2500 | 2500 – 3000 | 3000 – 3500 | 3500 – 4000 | 4000 – 4500 | 4500 – 5000 |
| Number of families | 24 | 40 | 33 | x | 30 | 22 | 16 | 7 |
Find the value of x and also, find the median and mean expenditure on milk.
