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Aptitude

Average

What do we mean by Average?

  • The average is a numeric value which is a single representation of a large amount of data.

  • The marks of the students of a class in a particular subject are averaged to give the average mark of the class.

  • The average of a set of values is equal to the sum of the values divided by the individual values.

  • Also, average is used in situations of changing values. The temperature of a place across the season is averaged to indicate the temperature of a place.

What is Average ?

  • Also, average is used in situations of changing values. The temperature of a place across the season is averaged to indicate the temperature of a place.

  • Hence, the average formula is:

    • Average = $\frac{Sum \; of \;the\; Observations\;}{Number\; of\; Observations\;}$

Average as Mean ?

  • Can be the average and mean be same ?

  • Mean is the average of group of data that are part of a consicutive data.

  • The average of a set of values is equal to the sum of the values divided by the individual values.

  • Also, average is used in situations of changing values.

    e.g. - The temperature of a place across the season is averaged to indicate the temperature of a place.

Advantages in Using Average

  • It is useful to represent a single value for a large amount of data.

  • If a student is reading a particular subject with n number of chapters in x hours.

    Then, the average time can be calculated for other similar subjects and chapters.

    This will help the student in time analysis.

  • If a child is participating in a particular sport, then the average is helpful for his\her coach to keep track of the changes in speed or energy.

  • The price of the shares of a company keeps changing every day. Here the average price of the share is quoted for reference.

Average in case of Speed and Velocity

What do we mean by Average Speed ?

  • It can be defined as total distance Travelled by a body in definite interval of time.

  • Average speed is calculated using the below formula :

    • $Average\; Speed\; = \frac{Total\; Distance\;}{Total\; Time\;}$

Case 1

  • When one travels at speed $a$ for half the time and speed $b$ for other half of the time.

  • Then, average speed is the arithmetic mean of the two speeds.

    • Average Speed = $\frac{a+b}{2}$

Case 2

  • When one travels at speed $a$ for half of the distance and speed $b$ for other half of the distance.

  • Then, average speed is the harmonic mean of the two speeds.

    • Average Speed = $\frac{2ab}{a+b}$

Case 3

  • When one travels at speed a for one-third of the distance, at speed b for another one-third of the distance and speed c for rest of the one-third of the distance

  • Then the average speed will be :

    • Average Speed = $\frac{3abc}{(ab+bc+ca)}$

Average Velocity

  • It can be defined as total displacement divided by total time. We can calculate Average Velocity by using the below formula :

  • Which depticts that the harmonic mean of the two speeds.

    • $Average\; Velocity\; = \frac{Displacement\;}{Total\; Time\;}$

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