| (i) For a given data with 110 observations the 'less than ogive' and 'more than ogive' intersect at (18, 20). The median of the data is P. |
| (ii) The curve is drawn by taking upper limit of class interval along x-axis and cumulating frequency along y-axis is Q than ogive. |
| (iii) The mean of 50 numbers is 18, the new mean will be R if each observation is increased by 4. |
| (iv) The mean of seven consecutive natural numbers is 20, then the largest number is S and smallest number of them is T. |
A)
P Q R S T 18 Less 22 23 17
B)
P Q R S T 20 More 25 22 16
C)
P Q R S T 18 More 22 24 18
D)
P Q R S T 20 Less 25 22 16
Correct Answer: A
Solution :
(i) The intersection point of less than ogive and more than ogive, the x-coordinate is the median. Median is 18. (ii) Less than ogive is drawn by taking the upper limit of class interval along x-axis and their corresponding less than cumulative frequencies along y-axis. (iii) Sum of 50 numbers\[=50\times 18=900\]; If each number is increased by 4, then new sum\[=900+4\times 50=1100\] \[\therefore \] New mean \[=\frac{1100}{50}=22\] (iv) Let seven consecutive numbers are x, \[x+1,\text{ }x+2,\text{ }....,\text{ }x+6\]. Mean \[=20\Rightarrow \frac{x(x+1)+....+(x+6)}{7}=20\] \[\Rightarrow \] \[\frac{7}{2}[2x+(7-1)1]=20\times 7\Rightarrow x+3=20\Rightarrow x=17\] Smallest number \[x=17\] Largest number \[=x+6=17+6=23.\]
You need to login to perform this action.
You will be redirected in
3 sec
