Page 288 - Start Up Mathematics_7

The median is calculated by taking the mean of the two middlemost terms, i.e.,

T + T n + 1 T + T 26 + 30
n
Median = 2 2 = 3 4 = = 28
2 2 2
Let’s summarize the method to find the median. In case of series of individual
observations, the following steps are used.

Step 1: Arrange the data in ascending or descending order.
Step 2: Find the number of observations n.
n + 1
Step 3: If n is odd, Median = Value of th term
2
n n
Value of c m th term + Value of c + m
1 th term
If n is even, Median = 2 2 2

Mode
Mode is value of the observation which occurs the maximum number of times in the data.

Let’s understand how to find mode and in which situations it is a relevant representative value of
the data.
A group of students belonging to different classes are going for a trekking expedition. The organizers
are providing them with special shoes whose sizes are: 4, 5, 5, 5, 5, 5, 6, 6, 7, 9
The average shoe size of 5.7 may not be appropriate for most of the students. The shoe size that
fits the maximum number of students is 5. Hence, the modal shoe size is worn by the maximum
number of students and is a true representative of the group.

Suppose the weights of 20 students of class VII in kg are as follows:
33, 30, 35, 28, 30, 35, 42, 35, 32, 35, 38, 35, 28, 40, 42, 31, 39, 35, 28, 40

Since the data is large, we convert it into frequency table.

Weight Tally bars f Weight Tally bars f

28 3 35 6
30 2 38 1

31 1 39 1

32 1 40 2
33 1 42 2

Clearly the maximum frequency 6 corresponds to the weight 35 kg. Hence, the modal weight is
35 kg. It means the maximum number of students in the class weigh 35 kg.

Example 7: Marks scored by 7 students in a test are: 37, 15, 40, 30, 58, 25, 40.
Find the range, mean, median and mode of the data.

Solution: We first arrange the data in ascending order as: 15, 25, 30, 37, 40, 40, 58
(i) Range = Largest value – smallest value = 58 – 15 = 43

Sum of the observations 245
(ii) Mean = = = 35
Tota umber of observations 7

280