ARITHMETIC MEAN
The average of numbers in arithmetic is known as the Arithmetic Mean or simply the mean of these numbers in statistics.
MEAN OF UNGROUPED DATA
The mean of n observations x1, x2, ...., xn is given by
where the symbol , called sigma stands for the summation of the terms.
Ex.14 The heights of 6 boys in a group are 142 cm, 154 cm, 146 cm, 145 cm, 151 cm and 150 cm. Find the mean height per boy.
Sol.
Ex.15 Find the mean of the first five multiples of 7.
Sol. The first five multiples of 7 are 7, 14, 21, 28 and 35.
MEAN FOR AN UNGROUPED FREQUENCY DISTRIBUTION
I. Direct Method
Let n observations consist of values x1, x2, ...., xn of a variable x, occurring with frequencies f1, f2, .... , fn respectively.
Then, the mean of these observations is given by :
Ex.18 The ages of 40 students in a class are given below :
Find the mean age of the class.
Sol. We prepare the table as given below :
Age (in years) Number of students 1;, xi
MEDIAN OF UNGROUPED DATA
Median : After arranging the given data in an ascending or a descending order of magnitude, the value of the middle-most observation is called the median of the data.
Method for Finding the Median of An Ungrouped Data
Arrange the given data in an increasing or decreasing order of magnitude. Let the total number of observations be n.
Ex.21 The marks of 13 students (out of 50) in an examination are:
39, 21, 23, 17, 32, 41, 18, 26, 30, 24, 27, 36, 9.
Find the median marks.
Sol. Arranging the marks in an ascending order, we have :
9, 17, 18, 21, 23, 24, 26, 27, 30, 32, 36, 39, 41
Here, n = 13, which is odd .
= Value of 7th term = 26.
Hence, the median marks are 26.
1. What is the difference between mean, median, and mode? |
2. When should I use mean, median, or mode? |
3. How do I calculate the mean, median, and mode of a set of numbers? |
4. What are some limitations of using mean, median, and mode? |
5. How are mean, median, and mode used in real-life situations? |
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