Rajasthan Board RBSE Class 11 Economics Notes Chapter 9 Median
→ Median is a place-related measure.
→ The value which occurs in the middle of a data-item series when the series is arranged in ascending order or descending order, is called the median.
Determination of Median
→ Individual Series – First, all the values are arranged in ascending or descending order with a view to convenience, the serial number of values should be written along with the values Then, the following formula is applied
M = Value of \(\left(\frac{N+1}{2}\right)\) th item; here N = number of items, M = Median
→ If the number of items in an individual series is even :
to determine the value of such series, the two integer serial numbers on either side of median term are added and the sum is divided by 2. This is the median value term.
Example 1. Find out the median from the following data- 62, 76, 84, 66, 70, 98, 56, 90, 78
Solution:
First of all the values are arranged in array or ascending order.
= value of the 5th item
Thus, the item-value of serial number 5 is the median-vlue.
M = 76
Example 2. Calculate median value from the following data- 30, 38, 70, 40, 36, 44, 56, 22, 30, 30
Answer:
On arranging data in ascending order
Thus, the item-value of serial number 5.5 is the median-vulue M = 37
Determination of median in discrete series- 1. Cumulative frequencies are determined as the first step. 2. Now, the median’s serial number is found using the following formula:
M = Value of \(\left(\frac{\mathrm{N}+1}{2}\right)\) th item.
Where N = ∑f
3. The value related to that cumulative frequency in which this serial number is included for the first time, is the median value.
Example 3. Find out the median value from the following data
Answer:
\(M=\left(\frac{N}{2}\right) \text { th item }=\left(\frac{127+1}{2}\right) \text { th item’s value }\)
= 64th item’s value
The 64th item is included in the cumulative frequency 84, Thus the value of 84 is median 16. Median =16 .
Determination of median in Continuous Series – 1. Cumulative frequencies are determined in the first step.
2. The median is calculated using the following formula:
\(\mathrm{M}=\left(\frac{\mathrm{N}}{2}\right) \text { th term } \)
3. When the median serial number is included in a cumulative frequency for the first time, the class related to that cumulative frequency is called the median class.
4. To determine the median value from median class, the following formulae are used:
(a) When datat-item series is ascending order:
\(M=1_{1}+\left[\frac{N / 2-c}{f}\right] \times i\)
(b) When data-item series is in descending order:
\(]M=1_{2}+\left[\frac{N / 2-c}{f}\right] \times i\)
M = Median
= class magnitude of median class (l2-l1)
f = frequency of median class
N = Total frequencies
c = Cumulative frequency of class proceeding median class
l2 = Upper limit of median class
l1 = Lower limit of median class
Example 4. Calculate median from the following series
Answer:
The 31st term is included in cumulative frequency 38. Thus the class in front of it (20-30) is the median
Quartile
When the series is divided into 4 equal parts, then it is called quartile. There are 2 actual quartiles in the series. The first quadrant (Q1 ), which is called the low quartile and the third quartile(Q3), is called the high quartile.
Quartile in Individual Series-
Firstly arrange series in arranging or array serial. Then from the following formula find out quartile-
Example 5. Find out Q1 and Q3 from the following data
Value 60, 42, 36, 50, 54, 58, 64, 70
Answer:
Quartile in Discrete Series – Cumulative frequency is calculated in this series. Then following formula will be used
Quartile in Continuous Series
(i) Firstly the cumulative frequency is found out in this series.
(ii) From the following formula the quartile class will be detected
(iii) Then quartile will be detected from the following formula-
Example 6. Find out low quartile (Q3), high quartile (Q3) and median from the below given series
Answer:
It is a cumulative series which will be converted into simple series firstly. Class interval is same in this.
