Rajasthan Board RBSE Class 11 Economics Notes Chapter 10 Mode
→ The English word “Mode” has its origin in the French word “La Mode”.
→ The meaning of ‘La Mode’ is fashion or custom that is largely prevalent.
→ Mode is that item in a data-item series whose frequency is the greatest.
→ Mode indicates that point where most number of items are centred.
→ Thus, mode is that value which occurs in a data-item series most number of times.
→ Mode is place-related mean.
→ Mode is determined in individual series, discrete series and continuous series.
1. Individual Series
The value that occurs the most number of times in a series is called the mode value. The following are the three methods of determining mode in an individual series.
(A) Converting individual series into discrete series : When many values are found twice or more than two times in an individual series, then the series should be converted into a discrete series.
Example 1. Find out the mode of the following series-
80, 88, 92, 100, 88, 68, 76, 88, 92, 84, 88
Answer:
By inspection, it is clear that the item-value 88 has occurred the most number of times (4 times). Thus, the mode is 44.
Z = 44.
(B) Converting into continuous series : When no value of an individual series occurs more than once then in such situation, the individual values are converted into continuous series and the class-interval with greatest frequency (mode class) should be determined.
(C) Estimation of Mode with the help of Arithmetic mean and median: If the arithmetic mean (X), median (M) and mode (Z), all three are to be determined, then the mode value can be estimated by the following formula based on inter-relationship of the three values:
Z = 3M-2\(\overline{\mathrm{X}}\)
2. Discrete Series
Following are the two methods of determining mode in discrete series –
(i) By inspection : The inspection method for mode determination should be used only when the frequencies of the discrete series are regular.
Example 2. Find out the mode weight from the following series-
Answer:
The frequencies are tegular in the above series. Thus, mode can be determined by inspection. The greatest frequency is 10 whose value is 27. Thus mode weight.
Z = 27 kg.
(ii) Grouping Method – Grouping method is used when the frequencies of data-items
series are irregular, since in such situation the greatest frequency cannot be known.
The objective of grouping is to ascertain the concentration point of frequencies in irregular frequency distribution.
First of all,a table is made in grouping method in which there are 6 additional columns for frequencies apart from variable values (x).
3. Determination of Mode in Continuous Series : First of all, like discrete series the mode is found out by the inspection or grouping method.
After finding the mode-class, the mode value can be calculated using the following formula.
\(Z=1_{1}+\frac{f_{1}-f_{0}}{2 f_{1}-f_{0}-f_{2}} \times i\)
Z = Value of mode, i = class interval, l1, = lower limit of mode-class f1 = frequency of mode-class, f0= frequency of class preceding mode-class f2 = frequency of class succeeding mode-class
- There are some merits and demerits in mode also.
- Mode is used by the common people in routine life to a great extent.
- Mode is a useful mean in business sphere, meteorology, life-sciences, consumer preferences, etc.