Page 285 - Start Up Mathematics_7

We note that the equal water level in both the beakers is 5 cm. Thus the average or mean level
of water contained in the two beakers in 5 cm.

5 cm

• Marks scored by Sanskruti in 5 subjects are 60, 70, 70, 80 and 90. She tells her friends that her
average marks are 74. How did she reach this figure, inspite of the fact that she has not scored 74
marks in any of the subjects?
Let’s find the sum of the marks obtained by Sanskruti in all the subjects, i.e., 60 + 70 + 70 + 80
370
+ 90 = 370. Now if we divide this sum by the total number of subjects, i.e., 5, we get = 74,
5
which gives us the average marks. It is also known as the arithmetic mean or simply the mean
of the data.
Thus we conclude that arithmetic mean is defined as the sum of all the values of the data divided
by the total number of values.

Arithmetic mean of n observations x , x , x , ..., x is given by:
n
3
2
1
Mean = Sum of all observations = x 1 + x2 + x3 + ... + xn
Total number of observations n
Example 1: Find the range of the following data:
18, 26, 92, 12, 86, 74 and 52.
Solution: First, arrange the data in ascending order,
i.e., 12, 18, 26, 52, 74, 86 and 92

We observe, Highest value of the data = 92
Lowest value of the data = 12

Thus, Range = Highest value – Lowest value = 92 – 12 = 80
Example 2: Pratibha studies for 3 hours, 4 hours, 7 hours and 2 hours on four consecutive days
before her final examination. How many hours did she study per day on an average?
Solution: The average time for which Pratibha studied during the four days is:

Total of study hours 3 + + + 2 16
7
4
Number of days = 4 = 4 = 4 hours
Thus, Pratibha studied for 4 hours per day on an average.
Example 3: The maximum daytime temperatures of Delhi in °C during 10 days of October are
as follows: 22, 21, 23, 25, 18, 27, 14, 16, 29, 25

(a) What maximum temperature was recorded on the hottest day?
(b) Find the least of the maximum daytime temperatures.
(c) What is the range of the data?

(d) What is the arithmetic mean of the maximum daytime temperatures?

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