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Concept of Representative Values - Average

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definition

Average: Average is a number that represents or shows the central tendency of a group of observations or data.

formula

Average = `"sum of the values of all the observations"/"total number of observations"`

notes

Concept of Representative Values - Average

  • Average is a number that represents or shows the central tendency of a group of observations or data.

  • Since average lies between the highest and the lowest value of the given data so, we say the average is a measure of the central tendency of the group of data.

  • Different forms of data need different forms of representative or central value to describe it.

  • The average is the sum of the values of all the observations divided by the total number of observations.

    ∴ Average = `" sum of the values of all the observations"/"total number of observations"`

  • Example,

  1. Isha spends an average of about 5 hours daily for her studies.
    ⇒ By average we understand that Isha, usually, studies for 5 hours. On some days, she may study for less number of hours and on the other days, she may study longer.

  2. The average temperature at this time of the year is about 40 degrees celsius.
    ⇒ The average temperature of 40 degrees celsius, means that, very often, the temperature at this time of the year is around 40-degree celsius. Sometimes, it may be less than 40 degrees celsius and at other times, it may be more than 40°C.

Example

A school conducted a survey to find out how far their students live from the school. Given below is the distance of the houses of six of the students from the school. Let us find their average distance from the school.
950 m, 800 m, 700 m, 1.5 km, 1 km, 750 m

Average = `"Sum of the distance between home and school for six students"/"Total number of students"`

= `(950 + 800 + 700 + 1500 + 1000 + 750)/6`

= `(5700)/6`

= 950 m

The average distance at which the students live from the school is 950 m.

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