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Numerical reasoning tests, especially numerical critical tests, introduce a large family of graphs and tables for representing numerical data.

Here is a helpful review of some graphs and tables that applicants always seem to have problems with.

**Content Table:**

- Graphs
- Line Graph
- Free Tables & Graphs Test
- Bar Graph
- Stacked Bar Graph
- Pie Chart
- Area Graph
- Radar Graph
- HLC/OHLC Graph
- Tables
- Statistical Information
- Financial Report Tables
- Everyday Tables
- Useful Resources

Graphs and tables are a common measure of presenting large amounts of data in a graphical, easy-to-understand way.

Since interpreting and analyzing graphs and tables is a task which requires both mathematical and reasoning skills, they are a favourite type of question in numerical reasoning tests.

graphs are used in numerical reasoning tests to convey complex data, but more often than not they are made to **pose** as complex while hiding the specific piece of information you need to answer the question.

The most important aspect of learning to solve graph question is knowing how disregard the noise and find the fastest course to what you need to verify the answer.

That is the simplest, most common type of graph. It normally presents data on two axes – horizontal and vertical. For each element on the horizontal axis, a value is given in the vertical axis. Usually, line graphs are used to show changes in a single element over time

Look at the example below:

The graph contains the following components:

Heading– the name of the graph (duh). Will usually reflect the axes. In our case: Prevalence of mental disorders (vertical axis) per Annum (horizontal axis).The vertical axis– this is the data the graph is intended to show. In our case, it's the prevalence of mental disorders.Horizontal axis– that is the graph's basis of comparison (in 95% of the cases you'll encounter, it'll be time). More generally, it presents the continuum along which the data changes. In our case, it's years.Labels– the names of the axes. These do not always appear, and you will need to understand the meaning of the axes from the heading or context.Legend– appears when more than one line appears on the same chart.

**Sample question:**

**Which of the following years had the lowest percentage of people who were not accepted?**

A. 2000

B. 2004

C. 2007

D. Insufficient data

Answer and explanation

The correct answer is **B**.

The diagram presents complementary data to the requested data - the percentage of students who were accepted to university.

The lowest percentage of people who were NOT accepted is the same as the year that had the highest percentage of people who were accepted, which according to the chart is 2004.

A bar graph presents data by categories in bars proportional to their respective value. Unlike a line graph, that has an element of continuum (like time), the categories in a bar graph are separated.

A bar graph may be vertical or horizontal. The vertical and category axes will naturally switch places:

Vertical |
Horizontal |

**Sample question:**

**Rich families spend ___________ of money on food as poor and middle class families combined.**

A. More than twice the amount

B. An equal amount

C. More than three times the amount

D. Half the amount

Answer and explanation

Rich families spend £5,500 monthly on food, whereas Poor families spend £1000 and middle class families spend £1,500. Combined poor and middle class families spend £2,500 on food, which is less than half the amount spent by the rich families. Therefore, rich families spend more than twice (but less than 3 times) as much money on food than poor and middle class families spend combined.

A stacked bar graph is similar to a bar graph, only that different data elements are presented on the same bar. These graphs are useful in visually and clearly revealing differences between categories or over time.

For instance, look at the graph below:

It is visually very clear that the sum of subsidiaries has declined drastically from 2007 to 2008, yet its share of the total investment has stayed rather similar (actually, it even grew slightly).

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Pie charts are used to present proportions of various elements. These elements can be measured in percent, money, numerical value (1,2,3…) or any other measurement.

The pie chart is one of the simplest graphs, and normally contains only 3 parts:

- Heading – we've already told you what that is…
- Legend – shows the distribution of colors on the chart
- The total amount to which the pie chart refers (if the chart presents percentages, well, you can guess for yourself what it'll be).

**Sample question:**

**What is the percentage of clubs income from the total income?**

A. 10

B. 20

C. 60

D. Cannot Say

Answer and explanation

The correct answer is B.

The data presented in the pie chart refers to millions of GBP. In order to convert it to percentage, we will first calculate the total income of all business.

(60+20+104+46+70) = 300

Now, let's calculate the percentage of clubs income from that amount:

(60/300) = 0.2 = 20%

Although they seem intimidating at first glance, area graphs simply combine the features of line graphs and stacked bar graphs. Each colored segment represents a series of data. Like bar graphs, area graphs may be 2D or 3D, vertical or horizontal.

There are two types of area graphs: stacked and non-stacked:

- In a non-stacked graph, each segment, representing one data series, overrides parts of another data series.
- In a stacked graph, each segment stands on its own and there is no override between series.

To illustrate, look at the graph below, in the red series in 2008:

In the non-stacked graph, the value of the red series in 2008 is 12 (all the way from the bottom). In the stacked graph, it is 2 = 12 – 10 (from the top of the previous series).

This type of area graph shows the relationship of the part to the whole, and is useful if you want to examine a cumulative effect.

Since distinguishing stacked from non-stacked 2D area graphs can be quite difficult, you will usually be provided with additional information that will allow you to conclude the graph type.

In these graphs, scale value grid lines are surrounding a central zero point. The numerical values can be mentioned once on one vertex, or, alternatively, each vertex can have its own values.

In this instance, in 2007, operational profit was £100,000,000.

High-low-close or open-high-low-close graphs are used for displaying daily fluctuations of stock prices. It is important to be familiar with the legend conventions of these graphs, which are quite simple.

In the HLC graph below, high values are marked by a triangle that intersects with the grid line, the low price is the bottom part of the line, and the close value can be inferred in this case only through a table which should accompany the graph.

In the OHLC graph below, the vertical rectangle marks the open/close values; when the box is dark, the open value was higher than the close value.

When the box is light, the open value was lower than the close value. The vertical line's edges represent the high/low values.

These graphs sometimes use different notations for marking the OHLC values, and can also include the volumes of stocks traded per day.

There are numerous types of tables that display numerical data. Numerical reasoning tests tend to contain a mixture of table themes such as population demographics, balance sheets, results of telemarketing surveys, etc.

Since the administrators' intention is to see how quickly you can analyse shifting sets of data, here are some popular tables used at numerical reasoning tests to further grow your knowledge in the area.

We advise you to go through these examples before starting to practise.

Let's look at some examples of frequently encountered statistical information tables:

The above table is quite simple. Numerical figures do not represent millions or thousands, rather absolute numbers. Furthermore, there are no columns that include percentages or ratios.

After using the orientation test - setting your eyes at a specific point within the data range/making sure you can understand the context - it is clear that the 'Total' column is the sum of 'All countries' + 'UK citizens'.

Here is another popular table, presenting demographic statistics and combining various types of data (area, numbers and rates):

**Sample question:**

**Which brewery produced the least in 2004?**

A. Uxbridge, UK

B. Malmo, Sweden

C. Torino, Italy

D. Ottawa, Canada

E. Canberra, Australia

Answer and explanation

The correct answer is **D**.

In order to determine which brewery produced the least in 2004, you need to use the 2005 Monthly Output and the Total Output as a Percentage of 2004. Since you are not told otherwise, you can assume the monthly output for any brewery is the same throughout the year, which means the brewery with the smallest monthly output will also be the one with the smallest yearly output. From this you can create the following equation:

Monthly Output in 2005 = Monthly Output in 2004 x Total Output as a Percentage of 2004

This equation can be converted to:

Monthly Output in 2004 = Monthly Output in 2005 / Total Output as a Percentage of 2004

Using the equation, you can find the monthly output of each brewery (since the data for all is in thousands of litres, you can omit the thousands from the calculation):

Uxbridge, UK: 12,000 / 120% = 12,000 / 1.2 = 10,000

Malmo, Sweden: 1,200 / 90% = 1,200 / 0.9 = 1,333.33

Torino, Italy: 8,000 / 70% = 8,000 / 0.7 = 11,428.57

Ottawa, Canada: 1,000 / 80% = 1,000 / 0.8 = 1,250

Canberra, Australia: 4,500 / 110% = 4,500 / 1.1 = 4,090.91

Therefore, the answer is Ottawa, Canada.**Shortcut**: You can save time by using estimation to eliminate some of the answer options. For the 2004 output to be low, the 2005 output should be as low as possible and the Total Output as a Percentage of 2004 should be as high as possible. Malmo and Ottawa’s low outputs stand out (with a fair Total Output as a Percentage of 2004). Therefore, you can eliminate all other options.

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The following table displays the results of an experiment. It is packed with figures, and the asterisks would probably be crucial for answering certain questions.

**Sample question:**

**Which of the following sub-groups achieved the highest average score at experiment 2?**

A. Young participants at the fluid ability test

B. Older participants at the vocabulary test

C. Young participants at the speed test

D. None of the above

Answer and explanation

The correct answer is **A**.

Although the question may not seem perfectly clear at first glance, when looking at the provided data and very different answer choices, it becomes clear we are requested to find the highest **relative score** (percentage).

Since each test has a different maximum score (as seen by the asterisks), we will calculate each sub-group's grade separately:

**A. Young participants at the fluid ability test:**

94.2/130) = 0.72 = 72%

**B. Older participants at the vocabulary test:**

(22.9/33) = 0.69 = 69%

**C. Young participants at the speed test:**

Since the test range is 1-100, the answer is already given in percentage and no calculation is needed. 65.4%

The highest grade of the three belongs to young participants taking the fluid ability test.

In these tables you would probably be asked to calculate some popular financial ratios - profit margins, growth rates, return on equity, etc.

Many of the leading financial services and consulting companies use numerical reasoning tests as part of their recruitment process.

Financial report tables are the most common type of table used in such tests. Familiarizing yourself with numerical tables is an essential part of the preparation for getting through the assessment tests.

Simpler cases might include the tables we come across with on a daily basis, e.g. nutritional values of foods, bills, travel expenses reports, etc.

JobTestPrep provides comprehensive numerical reasoning test practice and company-specific tailored PrepPacks, such as the Macquarie psychometric assessment preparation, as well as numerical reasoning practice specific to different test providers, for example, Cubiks test preparation.

Read more about numerical reasoning tests, numerical reasoning test tips and basic maths test.

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