Advertisements
Advertisements
Question
If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median.
Solution
Given that the ratio of mode and median of a certain data is 6:5. That is,
MODE : MEDIAN = 6.5
`⇒ (MODE )/(MEDIAN )= 6/5`
`⇒ 5 xx MODE = 6 xx MEDIAN`
`⇒MODE = 6/5 MEDIAN`
We know that
`MODE xx 3 xx MEDIAN -2 xx MEAN`
`⇒6/5 MEDIAN = 3 xx MEDIAN - 2 xx MEAN`
` ⇒ 2 xx MEAN = (3-6/5) MEAN `
`⇒ 2 xx MEAN = 9/5 MEDIAN`
`⇒ 2 MEAN = 9/10 MEDIAN`
`⇒ (MEAN)/(MEDIAN) = 9/10`
`⇒ MEAN : MEDIAN = 9:10`
APPEARS IN
RELATED QUESTIONS
In a mathematics test given to 15 students, the following marks (out of 100) are recorded:-
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
Find the mean, median and mode of this data.
Durations of sunshine (in hours) in Amritsar for first 10 days of August 1997 as reported by
the Meteorological Department are given below: 9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9
(i) Find the mean ЁЭСЛ ╠Е
(ii) Verify that = `sum _ ( i = 1)^10`(xi - x ) = 0
The mean of 5 numbers is 18. If one number is excluded, their mean is 16. Find the excluded number.
Find the values of n and X in each of the following cases :
(i) `sum _(i = 1)^n`(xi - 12) = - 10 `sum _(i = 1)^n`(xi - 3) = 62
(ii) `sum _(i = 1)^n` (xi - 10) = 30 `sum _(i = 6)^n` (xi - 6) = 150 .
Find the missing value of p for the following distribution whose mean is 12.58.
| x | 5 | 8 | 10 | 12 | p | 20 | 25 |
| f | 2 | 5 | 8 | 22 | 7 | 4 | 2 |
Find the median of the following data : 41, 43, 127, 99, 61, 92, 71, 58, 57 If 58 is replaced
by 85, what will be the new median.
The mean of a set of seven numbers is 81. If one of the numbers is discarded, the mean of the remaining numbers is 78. The value of discarded number is
If the mean of five observations x, x+2, x+4, x+6, x+8, is 11, then the mean of first three observations is
To draw a histogram to represent the following frequency distribution:
| Class interval | 5 – 10 | 10 – 15 | 15 – 25 | 25 – 45 | 45 – 75 |
| Frequency | 6 | 12 | 10 | 8 | 15 |
the adjusted frequency for the class 25 – 45 is:
The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting mean will be ______.
