The median of 14, 16, 17, p+4, 2p-2, 35,38,40 is 25. Calculate the mean.
Answers
Step-by-step explanation:
Given :-
The median of 14, 16, 17, p+4, 2p-2, 35,38,
40 is 25.
To find :-
Calculate the mean?
Solution :-
Given observations are :
14, 16, 17, p+4, 2p-2, 35,38,40
Number of observations (n) = 8
n = 8 is an even number
Finding the value of p through Median :-
We know that
If the number of observations is 'n' , an even number then median is the average of (n/2)th and [(n/2)+1]th observations.
n/2 = 8/2 = 4
4th observation = p+4
(n/2)+1 = 4+1 = 5
5th observation = 2p-2
Average of 4th and 5th observations
= [(p+4)+(2p-2)]/2
= (p+4+2p-2)/2
= (3p+2)/2
Median of the data = (3p+2)/2
According to the given problem
Median = 25
=> (3p+2)/2 = 25
=> 3p+2 = 25×2
=> 3p+2 = 50
=> 3p = 50-2
=> 3p = 48
=> p = 48/3
=> p = 16
Therefore, p = 16
Finding Mean :-
If p = 16 then p+4 = 16+4 = 20
If p =16 then 2p-2 = 2(16)-2=32-2 = 30
The observations are of 14, 16, 17, 20,30,
35,38,40
Sum of all observations
= 14+16+17+20+30+35+38+40
= 210
Number of observations = 8
We know that
Average = Sum of all observations /Number of all observations
=> Average = 210/8
=> Average = 26.25
Therefore, Mean = 26.25
Answer:-
Mean of the given data is 26.25
Used formulae:-
- If the number of observations is 'n' , an even number then median is the average of (n/2)th and [(n/2)+1]th observations.
- Average = Sum of all observations /Number of all observations
Points to know :-
- Median is the middle term of the given data when it is arranged in either ascending order or descending order.
- If the number of observations is 'n' , an even number then median is the average of (n/2)th and [(n/2)+1]th observations.
- If the number of observations is 'n' , an odd number then median is (n+1) /2th observations.
- Median divides the given data into two equal parts .
- Mean is the quotient when the sum of all observations are divided by the number of all observations.
- It is also called Average , Arithmetic Mean.