Mode and Mean of a data are $15x$ and $18x$, respectively. Then the median of the data is:
[1]
Find the missing frequency 'f' in the following table, if the mean of the given data is 18. Hence find the mode.
| Daily Allowance | Number of Children |
|---|---|
| 11-13 | 7 |
| 13-15 | 6 |
| 15-17 | 9 |
| 17-19 | 13 |
| 19-21 | f |
| 21-23 | 5 |
| 23-25 | 4 |
[5]
For some data $x_{1}, x_{2},......x_{n}$ with respective frequencies $f_{1},f_{2},......f_{n}$, the value of $\sum_{1}^{n}f_{i}(x_{i}-\overline{x})$ is equal to:
[1 mark]
The middle most observation of every data arranged in order is called :
[1 mark]
BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game. The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'.
| Numbers announced | Number of times |
| 0-15 | 8 |
| 15-30 | 9 |
| 30-45 | 10 |
| 45-60 | 12 |
| 60-75 | 9 |
Based on the above information, answer the following:
(i) Write the median class.
(ii) When first ball was picked up, what was the probability of calling out an even number ?
(iii) (a) Find median of the given data.
OR
(b) Find mode of the given data.
[4 marks]
The distribution below gives the marks obtained by 80 students on a test:
| Marks | Less than 10 | Less than 20 | Less than 30 | Less than 40 | Less than 50 | Less than 60 |
|---|---|---|---|---|---|---|
| Number of Students | 3 | 12 | 27 | 57 | 75 | 80 |
The modal class of this distribution is :
[1 mark]
If the value of each observation of a statistical data is increased by 3, then the mean of the data
[1 mark]
Case Study
India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country.
It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018:
| Rainfall (mm) | Number of Sub-divisions |
|---|---|
| 200-400 | 2 |
| 400-600 | 4 |
| 600-800 | 7 |
| 800-1000 | 4 |
| 1000-1200 | 2 |
| 1200-1400 | 3 |
| 1400-1600 | 1 |
| 1600-1800 | 1 |
Based on the above information, answer the following questions:
- (I) Write the modal class.
- (II) Find the median of the given data.
OR
(II) Find the mean rainfall in this season. - (III) If sub-division having at least 1000 mm rainfall during monsoon season, is considered good rainfall sub-division, then how many sub-divisions had good rainfall?
[4 marks]
Find the mode of the following frequency distribution:
| Class | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Frequency | 15 | 10 | 12 | 17 | 4 |
[2 marks]
For what value of x, is the median of the following frequency distribution 34.5?
| Class | Frequency |
|---|---|
| 0-10 | 3 |
| 10-20 | 5 |
| 20-30 | 11 |
| 30-40 | 10 |
| 40-50 | X |
| 50-60 | 3 |
| 60-70 | 2 |
[3 marks]
Following is the daily expenditure on lunch by 30 employees of a company:
| Daily Expenditure (in Rupees) | Number of Employees |
|---|---|
| 100-120 | 8 |
| 120-140 | 3 |
| 140-160 | 8 |
| 160-180 | 6 |
| 180-200 | 5 |
Find the mean daily expenditure of the employees.
[3 marks]
