**Arithmetic mean of ungrouped data :**

Arithmetic mean (AM) is one of the measures of central tendency which can be defined as the sum of all observations divided by the number of observations.

Formula to find arithmetic mean :

Mean

= Sum of all observations / Number of observations

Let us look into some example problems to understand the above concept.

**Question 1 :**

The marks obtained by 10 students in a test are 15, 75, 33, 67, 76, 54, 39, 12, 78, 11. Find the arithmetic mean.

**Solution :**

Mean = Total marks of 10 students / 10

= (15 + 75 + 33 + 67 + 76 + 54 + 39 + 12 + 78 + 11) / 10

= 460 / 10

= 46

**Question 2 :**

Find the mean of 2, 4, 6, 8, 10 , 12, 14, 16.

**Solution :**

Mean = Sum of given numbers / 8

= (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16) / 8

= 72 / 8

= 9

**Question 3 :**

John studies for 4 hours, 5 hours and 3 hours respectively on three consecutive days. How many hours does he study daily on an average?

**Solution :**

The average study time of John

= Total number of study hours / Number of days for which he studied

= (4 + 5 + 3) / 3

= 12 / 3

= 4 hours

Thus, we can say that John studies for 4 hours daily on an average.

**Question 4 :**

A batsman scored the following number of runs in six innings:

36, 35, 50, 46, 60, 55

Calculate the mean runs scored by him in an inning.

**Solution :**

To find the mean, we find the sum of all the observations and divide it by the number of observations.

Mean = Total runs / Number of innings

= (36 + 35 + 50 + 46 + 60 + 55) / 6

= 47

Thus, the mean runs scored in an inning are 47.

**Question 5 :**

The ages in years of 10 teachers of a school are:

32, 41, 28, 54, 35, 26, 23, 33, 38, 40

What is the mean age of these teachers?

**Solution :**

Mean age of the teachers

= Sum of age of teachers / Number of teachers

= (23 + 26 + 28 + 32 + 33 + 35 + 38 + 40 + 41 + 54) /10

= 350 / 10

= 35 years

**Question 6 :**

Following table shows the points of each player scored in four games:

Player |
Game 1 |
Game 2 |
Game 3 |
Game 4 |

A B C |
14 0 8 |
16 8 11 |
10 6 Did not play |
10 4 13 |

Now answer the following questions:

(i) Find the mean to determine A’s average number of points scored per game.

(ii) To find the mean number of points per game for C, would you divide the total points by 3 or by 4? Why?

(iii) B played in all the four games. How would you find the mean?

(iv) Who is the best performer?

**Solution :**

(i) Mean score of A = (14 + 16 + 10 + 10) / 4

= 12.5

Mean score of A per game is 12.5

(ii) To find the mean number of points per game for C, we have to divide the total points by 3.

Because he didn't participate in game 3. Total number of games he played is 3.

(iii) Mean score of B = (0 + 8 + 6 + 4) / 4

= 18/4

= 4.5

Mean score of B per game is 4.5

(iv) To choose the best performer, we have to find the mean score of each player.

Mean score of C = (8 + 11 + 13) / 3

= 32/3

= 10.6

Mean score of A per game is 12.5

Mean score of B per game is 4.5

Mean score of C per game is 10.6

Hence C is the best performer.

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