How To Find the Average in Maths
The average of numbers in a dataset is also known as the mean value. A dataset is a range of values measured, recorded or collected through a survey. The mean value of the dataset is calculated by adding up all the measured values (Summation), and then dividing the total by the number of values in the range. The formula for calculating the average can thus be derived:
Let Av be the average, and ∑x be the summation of x, and N be the number of values in the range. Therefore,
Av = Average.
∑x = Summation of X.
X = Value in the range (x1, x2, x3, x4…….)
N = Number of values in the range.
Av = (x1 + x2 + x3 + x4…)/N
Applications of Average Values in Real Life
The average of a dataset is the mean value which is representative of the dataset (sample or population). The average value is used for rough estimating purposes. The following are some of real life examples whereby the mean value is calculated in a statistical survey:
- Average height of males in a country
- Average height of females in a country
- Average age of voters in a country
- Average age of an audience (e.g. TV shows, sports, websites)
- Average monthly visitors (e.g. tourists, website visitors)
- Average income in a country
- Average middle class income
- Average upper class income
- Average lower class income
- Average academic achievement scores in a school, college, university or country
- Average I.Q in a country
- Average monthly sales in a year
- Average monthly profit in a year
- Average annual construction cost index in a location
- Average building cost per square metre in a location
- Average consumer price index in a city or country
- Average rent in a suburb, city, state or country
- Average house price in a suburb, city, state or country
- Average house price in middle class locations
- Average house price low-income locations
- Average house price in upper class locations
- Average mortality age in a country
- Average life expectancy in a country
- Average speed
- Average annual temperature in a country or region
- Average annual humidity in a country or region
- Average annual rainfall in a country or region
How to Calculate the Average – Problems and Solutions
Problem 1
There are 8 tomatoes in a pack weighing 1kg and priced at $26.99. Find the average weight and price of each tomato?
Solution:
Using ratios – If 8 tomatoes weigh 1000g, 1 tomato must be less than 1000g, therefore,
8 tomatoes = 1000g
1 tomato = X
Setting up a proportional equation,
>> X = (1 * 1000)/8
>> X = 125g
Answer: Each tomato weighs 125g
Calculating the price: If 8 tomatoes cost $26.99, then one tomato costs less. Therefore,
8 tomatoes = $26.99
1 tomato = X
Setting up a proportional equation,
>> X = (1 * $26.99)/8
>> X = $3.37
Answer: Each tomato costs $3.37.
Alternatively, we can use the weight to calculate the price of each tomato:
1000g = $26.99
125g = X
X = (125 * $26.99)/1000
X = $3.37
Answer : Each tomato costs $3.37.
Problem 2
In a class of 10 students, the following scores were obtained in the end of year biology examinations – 54, 60, 48, 72, 80, 55, 65, 50, 68, 75. Calculate the class average score?
Solution:
Using the formula Av = (x1 + x2 + x3 + x4…)/N
>> Av = (54 + 60 + 48 + 72 + 80 + 55 + 65 + 50 +68 + 75)/10
>> Av = (627)/10
>> Av = 62.7
Answer: The class average score is 62.7
Problem 3
The following hourly temperature readings were taken over 24 hours at a weather station :
21, 21.6, 21.9, 22.4, 22.7, 22.8, 23.1, 23.4, 23.7, 24, 24.6, 25.2,
25.2, 25.9, 25.8, 25.5, 25.9, 26.2, 26.5, 26.8, 27, 27.2, 27.8, 28
Find the mean daily temperature?
Solution:
Using the formula Av = (x1 + x2 + x3 + x4…)/N
>> Av = (21 + 21.6 + 21.9 + 22.4 + 22.7 + 22.8…….27.8 + 28)/24
>> Av = (594.2)/24
>> Av = 24.76
Answer: The mean daily temperature is 24.76 degrees Celsius.
Problem 4
In 2011, the monthly average rainfall in the Philippines was recorded as follows:
January – 27.9mm
February – 28.5mm
March -22.1mm
April – 20.7mm
May – 44.8mm
June – 51.2mm
July – 59.4mm
August – 44.9mm
September – 52.4mm
October – 50.1mm
November – 50.7mm
December – 44.4mm
Find the average annual rainfall in 2011?
Solution:
Using the formula Av = (x1 + x2 + x3 + x4…)/N
>> Av = (27.9 + 28.5 + 22.1 + 20.7 + 44.8…….50.7 + 44.4)/12
>> Av = (497.1)/12
>> Av = 41.43
Answer: The average annual rainfall was 41.43mm in 2011.
Problem 5
The ENR monthly building cost index in the USA (2019) is shown below:
January – 6107
February – 6108
March – 6110
April – 6110
May – 6112
June – 6118
July – 6131
August – 6147
September – 6147
October – 6169
November – 6179
December – 6199
Find the average annual building cost index?
Solution:
Using the formula Av = (x1 + x2 + x3 + x4…)/N
>> Av = (6107 + 6108 + 6110 + 6110 + 6112…….6179 + 6199)/12
>> Av = (73637)/12
>> Av = 6136.4
Answer: The average annual building cost index is 6136.4
Problem 6
In five annual competitions, an athlete took the following times to run a 200m sprint – 22.5, 23, 22.2, 23.1 and 22.7 seconds. What is the athlete’s average speed per second?
Solution:
Using the formula Av = (x1 + x2 + x3 + x4…)/N
>> Av = (22.5 + 23 + 22.2 + 23.1 + 22.7)/5
>> Av = (113.5)/5
>> Av = 22.7 seconds
The athlete’s average finishing time is 22.7 seconds.
The athlete’s average speed per second is >> 200m/22.7 seconds = 8.81 m/s.
Problem 7
A fast food outlet sells burgers at $2.99 each. The following orders were made in a particular week:
Sunday – 700
Monday – 900
Tuesday – 860
Wednesday – 875
Thursday – 800
Friday – 750
Saturday – 915
Calculate the average daily sales revenue?
Solution:
Using the formula Av = (x1 + x2 + x3 + x4…)/N
>> Av = (700 + 900 + 860 + 875 + 800 + 750 + 915)/7
>> Av = (5800)/7
>> Av = 828.57 To the nearest whole number >> 829 burgers.
The average number of burgers sold in a day is 829.
The average daily sales revenue is >> 829 x $2.99 per burger = $2478.71