Calculating Frequency

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Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency.

The SI unit of frequency is the hertz (Hz), defined as one cycle per second.

-Source Wikipedia.

The method for calculating frequency is explained by the following examples which is given as below:
Example on Calculating Frequency

The example used to calculating frequency are given as follow:

Using the key: C = Cricket, V = Volleyball, S = Swimming, each letter below indicates a student joining the sports team.

C C V SV C S S C V

V V C S C C S V C V

a) Construct a frequency table for the data.

b) Determine which team has the highest frequency and which team has the lowest frequency.

c) Calculate the percentage of students who joined the Cricket team.

Sol:

a) First, we tally the student count by the team they belong to. The total number of counts each Team receives is the frequency of the number of students joining ...
... that team. We can construct the data in the frequency table.

b) From the frequency table, we can determine which team has the highest frequency and which team has the lowest frequency. Cricket is the team with the highest frequency and swimming is the team with the lowest frequency.

c) Percentage of students who joined the Cricket team

= `6 / 16` x 100%

= 37.5%
Practice Problem on Calculating Frequency:

The practice problem for calculating frequency is given as follow:

Using the key: B = Book, P = Pen, T = Table, each letter below indicates a student studying things.

B B P T P B T T P

P P B T B B T P B P

a) Construct a frequency table for the data.

b) Determine which thing has the highest frequency and which thing has the lowest frequency.

c) Calculate the percentage of students who studied by using Book.

Sol:

a) First, we tally the student count by the team they belong to. The total number of counts each thing receives is the frequency of the number of students studying thing. We can construct the data in the frequency table.
F
rom the frequency table, we can determine which team has the highest frequency and which team has the lowest frequency. Cricket is the team with the highest frequency and swimming is the team with the lowest frequency.

c) Percentage of students who joined the Cricket team

= `8 / 20` x 100%

= 40%

Mean is defined as establishing the difference among the specified group of scores. The mean is nothing but average of the scores. It is simple to calculate: now add up all the scores, and then divide through how many scores there are. Formulas for Calculating mean score is given below that,

`barx =(sum(x))/n`

Example:

Calculating the mean score of 3, 8 and 10?

Solution:

3 + 8 + 10 = 21

= 21 ÷ 3

= 7

Mean score of 3, 8 and 10 is 7.

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Calculating Mean Score:

Steps for Calculating mean score:

Obtain the amount for every the scores in the known in the facts set.

Obtain the mean for the known set of n scores in the known set of facts.

Mean:

The mean is nothing but average of the scores.

For example, the group of scores is 4, 7, 4, 3, and 7.

Now we position the amount of group of scores: 4 + 7 + 4 + 3 + 7 = 25

Count of scores: 5

So the Mean score of 4, 7, 4, 3, and 7 is 25/5 = 5.
Worked Examples for Calculating Mean Score:

Example 1:

Calculating the mean scores of 9, 13 and 17?

Solution:

Step 1:

Average of the scores:

Add all scores

9 + 13 + 17 = 39

Step 2:

Then divide through total scores

= 39 ÷ 3

= 13

So the Mean score of 9, 13 and 17 is 12.

Example 2:

Calculating the mean scores of 10, 12, 14, 16, 18 and 20?

Solution:

Step 1:

Average of the scores:

Add all scores

10 + 12 + 14 + 16 + 18 + 20 = 90

Step 2:

Then divide through total scores

= 90 ÷ 6

= 15

So the Mean score of 10, 12, 14, 16, 18 and 20 is 15.

Example 3:

Calculating the mean scores of 3, 6, 9, 12, 15, 17 and 19?

Solution:

Step 1:

Average of the scores:

Add all scores

3 + 6 + 9 + 12 + 15 + 17 + 19 = 81

Step 2:

Then divide through total scores

= 81 ÷ 7

= 11.57

So the Mean score of 3, 6, 9, 12, 15, 17 and 19 is 11.57.

Example 4:

Calculating the mean scores of 5, 10, 15, 20, 25, 30, 35 and 40?

Solution:

Step 1:

Average of the scores:

Add all scores

5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 = 180

Step 2:

Then divide through total scores

= 180 ÷ 8

= 22.5

So the Mean score of 5, 10, 15, 20, 25, 30, 35 and 40 is 22.5.
Practice problems for Calculating mean score:

Practice Problem 1:

Calculating the mean scores of 6, 12, 15, 22, and 40?

Answer: The mean value is 19.

Practice Problem 2:

Calculating the mean scores of 7, 10, 12, 14, 18, and 20?

Answer: The mean value is 13.5

Practice Problem 3:

Calculating the mean scores of 8, 9, 12, 13, 18, 19 and 22?

Answer: The mean value is 14.43

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