The mean of the observations 48, 42, \(x+17\), \(x+15\), \(x+20\), 60 and 58 is 53. Then, the median of these observations is:
54
The mean of the 7 observations is 53, so their total sum is \(53\times7=371\).
The known values add up to \(48+42+60+58=208\), and the remaining three terms add up to \((x+17)+(x+15)+(x+20)=3x+52\).
So \(208+3x+52=371\), which gives \(3x=111\) and \(x=37\).
Substituting \(x=37\), the three unknown observations become \(x+17=54\), \(x+15=52\) and \(x+20=57\).
Arranging all seven observations in order gives 42, 48, 52, 54, 57, 58, 60 — with 7 values, the median is the 4th value, which is 54.
Hence, the median of these observations is 54.
Similar Questions
Numbers 12, 13, 14, ..., 101, 102 and 103 are written on slips (one number on one slip) and put in a box. A slip is then taken out from the box at random. What is the probability that the selected slip bears a number divisible by 7?
A bag contains 5 white and 4 red balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is not red ?
If each observation of the data is increased by 5, then the new mean :
Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
Find the mode and median of 3, 4, 5, 5, 3, 6, 7, 3, 5, 5, 6.
A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
Find the mean of first 5 two-digit multiples of 4.
