Back to: MATHEMATICS SS1
Welcome to class!
In today’s class, we will be talking about the calculation of range, median and mode of ungrouped data. Enjoy the class!
Calculation of Range, Median and Mode of Ungrouped Data
Ungrouped data is the type of distribution in which the data is individually given in a raw form. For example, the scores of a batsman in last 5 matches are given as 45,34,2,77 and 80.
The range is defined simply as the difference between the maximum and minimum value in the distribution.
Range of ungrouped data
We know now that range is the difference between the maximum and minimum value. Hence for ungrouped data, we arrange the series in ascending or descending order. This helps us to select the highest and lowest values in the distribution. Henceforth, we simply subtract the minimum value from the maximum value.
For example – The marks of a student in 5 tests of the chapter statistics are(out of 20)- 11, 14, 16, 13 and 18. Arranging them in ascending order- 18, 16, 14, 13 and 11. The range of the data is given as- 18-11=7.
Range= Maximum value – Minimum value
| Median M = (n+12)th value of observation in ascending order |
| 3. The mode is that value of the observation which occurs maximum number of times. |
Example
1. Calculate the Median, Mode from the following data: 3,13,11,15,5,4,2,3,2
- Median:
Observations in the ascending order are:
2,2,3,3,4,5,11,13,15
Here, n=9 is odd.
M = value of (n+12)th observation
M = value of (9+12)th observation
M = value of 5th observation
M =4
- Mode:
In the given data, the observation 2,3 occurs the maximum number of times (2)
∴Z=2,3
2. Calculate the Median, Mode from the following data: 85,96,76,108,85,80,100,85,70,95
- Median:
Observations in the ascending order are: 70,76,80,85,85,85,95,96,100,108
Here, n=10 is even.
M=Value of(n2)thobservation+Value of(n2+1)thobservation2
M =Value of(102)thobservation+Value of(102+1)thobservation2
M =Value of5thobservation+Value of6thobservation2
M =85+852
M =85
- Mode:
In the given data, the observation 85 occurs the maximum number of times (3)
∴Z=85
In our next class, we will be talking about Mean Deviation, Variance and Standard Deviation. We hope you enjoyed the class.
Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.
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Come again on the median