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Solution: Mean of 6 numbers = 45
\ Sum of 6 numbers = 45 × 6 = 270

(Q Sum of the observations = Mean × Number of observations)
After one number is excluded, the mean of remaining 5 numbers = 38
\ Sum of remaining 5 numbers = 5 × 38 = 190
Thus, the excluded number = 270 – 190 = 80

Mode

Let us take an example, a boutique deals with different kinds of women's apparel. The most popular
dress size they sell is the size 85 cm.
The owner is concerned about the number of dresses of different sizes sold. She is however looking
at the dress size that is sold the most.
The highest occurring demand size of dresses is 85 cm. This is another
representative value for the data. This representative value is called the
mode of the data.
Thus, the mode of a set of observations is the observation that occurs
most often.
Or, the mode of data is the observation that occurs maximum numbers
of times.
Or, mode is the value of observations for which the frequency is maximum.
Example 13: Find the mode of the following data: 11, 3, 7, 4, 2, 4, 3, 5, 4, 8, 11, 13, 4.
Solution: Arranging the numbers in ascending order, we get
2, 3, 3, 4, 4, 4, 4, 5, 7, 8, 11, 11, 13
Clearly, observations 4 occurs maximum number of times that
is four times. From the adjoining example,
Thus, the mode of the given observations is 4. Note: we understand that mode
Example 14: Given below are the number of children in 25 may not be unique i.e., there
may be a data where there
families: 3, 1, 1, 0, 1, 2, 2, 2, 4, 2, 2, 1, 0, 1, 2, 4, 4, 3, 3, 2, 1, 3, 1, 1, 2. are more than one mode.
Find the modal number of children of a family.

Solution: Here the number of observations is large. In such cases we tabulate the data.
So, arrange the given data using frequency distribution table.

Number of Children Tally Marks Number of families
in a family (Frequency) Quick Check
0 2 1. What is the mode of the height
1 8 of the students of your class?
2 8 2. The marks (out of 50) in maths
3 4 unit test for a batch of 12
4 3 students are as follows: 31, 37,
35, 38, 42, 23, 17, 18, 35, 25, 35,
It is clear from the above table, the value of 2 and 1 occurs 29. What is the mean and mode
most frequently, i.e., 8 times. of marks of the batch? Which is
So, 1 and 2 are the mode of the given data. greater?

313 Data Handling