Page 284 - Start Up Mathematics_7

The data in this form is called raw or ungrouped data. In this form the data is not easy to understand

and interpret. The data becomes meaningful if we arrange it in ascending or descending order of
magnitude called an array. The above data arranged in ascending order is:
4, 5, 7, 10, 13, 17, 23, 30, 41, 42, 55, 69, 74, 86, 90, 93, 98, 102, 110, 115, 118

In this form, we can analyze the data very fast and know that the highest runs scored is 118 and
the minimum runs scored is 4. Not only this, there are a total of 4 centuries scored and 10 players
failed to reach the half century mark.

The spread in the data called its range is the difference between the highest and the lowest scores.
With the data in ascending order, we can immediately determine its range as follows:

Range = Highest value – Lowest Value = 118 – 4 = 114 runs
Now, if we arrange the above data in the form of frequency distribution using tally marks, it
becomes capable of being analyzed further.

From the table given alongside we can get some
more information like, Runs scored Tally marks Frequency
1–20 6
• only 2 batsmen have scored runs in the interval
61–80. 21–40 2

• 8 players have scored above 80 runs. 41–60 3
• the frequency is more or less uniformly 61–80 2
distributed with majority scoring upto 20 runs. 81–100 4

The data in this form is capable for further 101–120 4
statistical treatment and hence underlines the
importance of organizing the collected data.

Measures of Central Tendency
There are certain single values that lie within the range of the data and are representative of all the

values of the data. These are known as central tendencies. The three central values of the data are:
mean, median and mode. These figures give some sort of central value, i.e., either the average or
what divides the data into equal halves or the most frequently occurring value of the data.

Arithmetic mean

Let’s consider a few examples to understand the concept of arithmetic mean:

• Consider two similar beakers containing water up to a
level of 3 cm and 7 cm respectively (Fig. 1). Can you 7 cm
guess the level of water in each beaker if both the beakers
share water equally? The answer to this question lies in 3 cm
what is called the arithmetic mean. It gives the value if
the unequals are made equals by sharing. Pour water from Fig. 1
the beaker containing more water into the other till the water level in the two beakers is same.

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