There are 10 observation arranged in ascending order as given below: 45,47,50,52,x,x+2,60,62,63,74. The median of these observation is 53 . a) Find the value of x . b) Find the mean.
Answers
• given : meadian value = 53
a)• if n is odd ,the median value is the middle most value .
• if n is even ,the median value is the average of the 2 middle values.
• here n= 10 ,which is even ,so the median is the average value of the 2 middle values
• here the 2 middle values are x and x+2, so the median value = x+x+2
We know that median value is 53
53= x + x+2
We get , x = 25.5
So the value of x is 25.5
• if x = 25.5, then x +2= 27.5
• thus the observations are 45,47,50,52,25.5,27.5, 60,62,63,74
b) • the mean the sum of all the observations divided by the number of observations
• the mean=(45+47+50+52+25.5+27.5+60+62+63
+74)/10
= 50.6
Answer:
x = 52
median = 52
mode = 52
mean = 59.9
Given:
observation- 45,47,50,52,x,x+2,60,63,74
median-53
Step-by-step explanation:
median = The number appearing exactly at the middle position in ascending or decending order
therefore, median = x + x+2 /2
53 = 2x + 2 /2
2 × 53 = 2x + 2
106 = 2x +2
106 - 2 = 2x
2x = 104
x = 52
mode = the score which is repeated maximum number of times
therefore, mode = 52
mean = the average of all observation
therefore, mean =
45+47+50+52+52+54+60+62+63+74
10
= 559 / 10
= 59.9
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