Statistical estimation - Examples, Exercises and Solutions

Estimation

In fact, estimation allows us to guess (hence the redundancy) the supposed result, without performing the exact calculation.
That is, in certain cases, we don't need to know the solution precisely, a rough idea is sufficient to solve a particular mathematical problem.

Sometimes we are asked to compare mathematical expressions, draw deductions from one exercise to another, round numbers to simplify a calculation, and other similar tasks. 

For example:

It can be estimated that half of 1603 is approximately 800.

50% of 1603  Estimation

Suggested Topics to Practice in Advance

  1. How to Calculate Percentage

Practice Statistical estimation

Exercise #1

Approximately what is 625 \frac{6}{25} as a percentage?

Video Solution

Step-by-Step Solution

We look for the closest fraction to be able to divide the numerator by the denominator:

525 \frac{5}{25}

We break down the denominator into a multiplication exercise:

55×5 \frac{5}{5\times5}

We simplify:

15 \frac{1}{5}

We convert the fraction into a percentage

15×100=1005= \frac{1}{5}\times100=\frac{100}{5}=

20% 20\%

Answer

20%

Exercise #2

Approximately what is 145 \frac{14}{5} as a percentage?

Video Solution

Step-by-Step Solution

We are looking for the closest fraction to be able to divide the numerator by the denominator:

155=3 \frac{15}{5}=3

Convert the fraction into percentage:

3×100=300 3\times100=300

300% 300\%

Answer

300%

Exercise #3

Approximately what is 50204 \frac{50}{204} written as a percentage?

Video Solution

Step-by-Step Solution

Find the closest fraction so we can divide the numerator by the denominator:

50200 \frac{50}{200}

We break down the denominator into a multiplication exercise:

550×4 \frac{5}{50\times4}

We simplify:

14 \frac{1}{4}

We convert the fraction to a percentage:

14×100=1004= \frac{1}{4}\times100=\frac{100}{4}=

25% 25\%

Answer

25%

Exercise #4

Approximately what is 17 \frac{1}{7} written as a percentage?

Video Solution

Step-by-Step Solution

The easiest way to convert a fraction to a percentage is to convert the denominator to 100.

However, 100 is not in the multiplication table of 7, so in this exercise, we will use an estimation.

First, we will take 7 to a close number that can be easily converted to 100 - 20.

We know that 20*5 is 100 and that 7*3=21.

Although 21 is not equal to 20, it is approximately close.

Therefore, we will first multiply the entire fraction (the numerator and the denominator) by 3 to reach the denominator of 20.

Then we multiply the denominator and the numerator by 5 to reach the denominator 100.

We will arrive at a result of 15/100, that is 15%, which is the correct answer!

Answer

15%

Exercise #5

What percentage does the shaded area of the figure represent?

Video Solution

Step-by-Step Solution

It can be said with certainty that the shaded area is larger than half of the shape.

That is, the shaded part is more than 50%.

Therefore, we can disregard answers B and D.

The unshaded part is greater than 1% of the figure; it is not possible for 100 such parts to form the complete shape, therefore, we can disregard answer C.

Therefore, the correct answer must be 80%.

Answer

80%

Exercise #1

Organise the following into two groups of values less than 12% and values greater than 12%.

11100,0.1,0.13,640,20% \frac{11}{100},0.1,0.13,\frac{6}{40},20\%

Video Solution

Step-by-Step Solution

12%=12100=0.12 12\%=\frac{12}{100}=0.12

Now we will convert all values into percentages and see which are greater and which are less than 12%.

640×2.52.5=15100=15% \frac{6}{40}\times\frac{2.5}{2.5}=\frac{15}{100}=15\%

11100=11% \frac{11}{100}=11\%

0.1=10100=10% 0.1=\frac{10}{100}=10\%

0.13=13100=13% 0.13=\frac{13}{100}=13\%

Now we can observe which are greater and less than 12%.

Answer

0.13,\frac{6}{40},20\%>12\%

\frac{11}{100},0.1<12\%

Exercise #2

Approximately what is 3470 \frac{34}{70} written as a percentage?

Video Solution

Answer

50%

Exercise #3

Approximately what is 8011 \frac{80}{11} written as a percentage?

Video Solution

Answer

800%

Exercise #4

Approximately what is 19 \frac{1}{9} as a percentage?

Video Solution

Answer

10%

Exercise #5

Approximately what is 1561 \frac{15}{61} written as a percentage?

Video Solution

Answer

25%

Exercise #1

Approximately what is 1150 \frac{11}{50} written as a percentage?

Video Solution

Answer

20%

Exercise #2

What is the approximate percentage of 617 \frac{6}{17} ?

Video Solution

Answer

33.33%

Exercise #3

Approximately what is 134 \frac{13}{4} written as a percentage?

Video Solution

Answer

300%

Exercise #4

Approximately what is 2082 \frac{20}{82} written as a percentage?

Video Solution

Answer

25%

Exercise #5

Approximately what is 19048 \frac{190}{48} as a percentage?

Video Solution

Answer

400%