**Arithmetic mean problems :**

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.

**Example 1 :**

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.

**Example 2 :**

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.

**Example 3 :**

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

**Example 4 :**

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.

After having gone through the stuff given above, we hope that the students would have understood "Arithmetic mean problems".

Apart from the stuff given above, if you want to know more about "Arithmetic mean problems",please click here

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Time and work word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**