In this article I will talk about the concept of frequency and percentage frequency, and then explain how to use charts and diagrams to illustrate them: pie and bar charts for nominal and histograms - for numerical data.

**Frequency tells us how often some category occurs in our data**. It is important to understand that the category can have either nominal or numerical value. With nominal ones it is quite straightforward: for example, if there are four people with blue eyes in a room of 12 people, then it means that the frequency of blue-eyed people in this room is four. Here, the category is*blue eyes*(in this data other categories could be, for example,*green*,*brown*and*grey*eyes).Confusion may occur when frequency for the

*numerical*data is being calculated, simply due to the fact that both figures are presented in numbers. For example, IQ is measured numerically, which means its value is determined by a score (a number). So, if five of those 12 people have an IQ of 130, we can say that frequency of the people with IQ of 130 in the room is five. Thus, the IQ score of 130 is a category which occurs five times in the data (here, other categories could be*IQ of 100*,*IQ of 90*,*IQ of 80*etc.)## Percentage Frequencies

Frequency provides much clearer picture when is expressed in percentage rather than in a number. So, let's see how we could calculate this to use in our data analysis later.

Let us look at the blue-eyed people in the room mentioned above. The category frequency, as we said earlier, equals 4. The total frequencies equals 12. Now, to calculate the percentage we need to multiply the category frequency by 100 and then divide it by the total frequency. Thus:

category frequency * 100 / total frequency = 4*100 / 12 = 400/12 = 33.(3)%

In other words, the frequency of people with blue eyes in the room of 12 people is 33.3% (precisely a third)

Let us look at the blue-eyed people in the room mentioned above. The category frequency, as we said earlier, equals 4. The total frequencies equals 12. Now, to calculate the percentage we need to multiply the category frequency by 100 and then divide it by the total frequency. Thus:

category frequency * 100 / total frequency = 4*100 / 12 = 400/12 = 33.(3)%

In other words, the frequency of people with blue eyes in the room of 12 people is 33.3% (precisely a third)

## Charts and diagrams for frequencies: nominal data

Our blue-eyed peeps

**1. Pie diagram**

To make your statistics data easy to grasp and understand, it is a good idea to show the percentage frequencies using a pie diagram. To make it true to the data, you would need to calculate the angles for your pie slices. It is done simply by multiplying each of your percentage frequencies by 3.6 (since there are 360 degree in a full circle). Thus:

33.3% * 3.6 = 119.998 = rounded up to 120 degrees, which is a third of 360 degrees.

BAD pie

*Tips for a good pie:*

> A pie diagram won't work well if there are too many

categories (see the picture) - it looks like a mess and

does not communicate the data clearly.

> It won't work if one of the slices is HUGE and the

others can be barely seen!

> Make it beautiful by assigning different colours to

slices and marking them clearly.

**2. Bar chart**

So what do you use if the pie is no good for your purposes?

Use the bar chart instead. The heights of the bars make the trends very easy to see. However, it is

**very important to remember**that the bars are NOT scores, but frequencies of categories; hence, there always should be equal spaces between them to show that they are

*not*points on a single numerical scale. In the picture, for example, the bars could represent such categories as subjects' occupations or eyes colours.

## Charts and diagrams for frequencies: numerical score data

**Histogram**

Histogram looks quite similar to a bar chart, however there is one key difference: its bars represent scores on a single numerical scale. Thus, there are no spaces in between the bars.

Let us look at those 12 people again. Their IQ scores can be shown in a histogram. Now, there are too many options for the IQ values - we couldn't draw a bar for each of them, and if we did it would be quite useless. So, what we can do instead is to divide all the results into broader categories, such as:

1. 60 and below

2. 60-80

3. 80-100

4. 100-120

5. 120-140

6. 140 and above

In such a way, the histogram will only contain 6 bars and will give a clear picture of the trends. The frequencies appear on the left, while categories should be marked below the corresponding bars.