find the median of 12,16,12,6,18,2,4
Answers
Answer- The above question is from the chapter 'Statistics'.
Statistics- It is a branch of Mathematics dealing with the collection and analysis of data which can be single as well as grouped.
Mean, median and mode are called 'Measures of Central Tendency'.
Mean: Average of a given data is called mean.
Median: The middle most value of a given data is called median.
Mode: The most frequently occurring value in a given data is called mode.
What is ungrouped data?
⇒ Single data is called ungrouped data.
For example- Marks obtained by a student in class X in 5 subjects (out of 80): 60, 70, 55, 80, 65.
Finding median-
Median = (n+1)th term/2 where n= number of observations (n= odd)
Median = (1/2) (n/2)th term+ (n/2 + 1) th term where n= number of observations (n= even)
What is grouped data?
⇒ A continuous data and a single data dependent on each other is called grouped data.
Formula of median in Grouped data:
Median = l + [(N/2 - CF)/f] h
where l = lower limit of median class
N = Total sum of frequencies
CF = Cumulative frequency just before median class
f = Frequency of median class
h = Height of class intervals
Given question: Find the median of 12 , 16, 12 , 6 , 18, 2 , 4.
Solution: The above data is single data.
Arranging data in ascending order, we get,
2 , 4 , 6 , 12 , 12 , 16 , 18
Number of terms = 7 (odd)
Median = (n + 1)th term/2 where n = number of observations (n = odd)
Median (7 + 1)th term/2
Median = 8th term/2
Median = 4th term
Median = 12