How To Find the Average of Numbers in a Data Set – Maths and Statistics

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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

Mathematics Average Formula Mean Value

Mathematics Average Formula Mean Value

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


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