Continuing our discussion on IR, let’s look at a graph today and learn how to infer from the data given in it. You may not need to do too many calculations because the options in the drop down menu may allow you to approximate i.e. the options may be quite far apart. Also, you will need to segment the graph into regions using imaginary vertical lines e.g. number of household spending less than 2 hrs at the mall in the graph given below.

The segmentation may not be perfect and hence you may not get the exact answer. The options need to have some scope of error and that is another reason why the options may be far apart. Anyway, the purpose of the graphs is to depict relative trends so exact values are not important.

**Question**: In a survey of 60 households, the following data was obtained. It gives the relation between ‘annual household income’ and ‘number of hours spent in shopping malls per week’.

1. No household with an annual income of greater than $135,000 spends more than ___ hours in the shopping malls per week.

(A) 3 (B) 5 (C) 6

The households with income above $135,000 are the ones lying above the solid blue line. None of them spends more than 6 hrs at the mall. Note that if you are unsure of where the red point lies (less than or greater than 5), it doesn’t matter. You know for sure that all points lie to the left of 6 and you can have only one correct answer. Hence the red point must lie to the right of 5.

**Answer (C)**

2. From the households surveyed in the graph above, the pool that spends maximum time on average at the mall is the one with the annual household income between____

(A) 75,000 – 90,000 (B) 90,000 – 105,000 (C) 105,000 – 120,000

The average time spent by households in the $75,000 – 90,000 range will be to the left of the red dot. Note that there is a point to the extreme left of the red dot and one to the extreme right. Both these points are almost equidistant from the red dot. There is another dot slightly to the left of the red dot. Hence the average will be very near the red dot but to its left.

The average time spent by households in the $90,000 – 105,000 range will be around the green dot. Look at the two dots to the far left of the green dot. The three dots to the right of the green dot are much closer to the green dot. Hence, if anything, the average will be to the left of the green dot, not to its right.

The average time spent by households in the $105,000 – 120,000 range will be close to the orange dot. It will be to the right of the orange dot, not to the left.

The orange dot is the rightmost and hence the average in the range 105,000 – 120,000 will be the highest.

**Answer (C)**

3. Number of households spending more than 6 hrs per week in a mall is around ____% of the number of household spending less than 2 hrs per week at the mall.

(A) 10% (B) 30% (C) 50%

We need to segment the graph into three sections – less than 2 hrs, between 2 to 6 hrs and more than 6 hrs.

Number of households that spend less than 2 hrs per week in a shopping mall – around 21

Number of households that spend more than 6 hrs per week in a shopping mall – 7

Number of households that spend more than 6 hrs per week is about 30% of the number of households that spend less than 2 hrs per week.

**Answer (B)**

4. Number of households earning more than $135,000 annually and spending less than 3 hrs per week at the mall is around ____% of the total number of households surveyed.

(A) 10% (B) 30% (C) 40%

Again we segment the graph such that the top left corner comprises of households with annual income more than $135,000 but spending less than 3 hrs per week at the mall. On counting them, we find that there are 18 such households. We also know that total there are 60 households surveyed. Hence the required percentage is 18/60 i.e. 30%.

**Answer (B)**

Hope you have a better grasp of graphs now. More to come shortly!

*Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the **GMAT** for Veritas Prep and regularly participates in content development projects such as this blog!*

@Lala

“Look at the two dots to the far left of the green dot. The three dots to the right of the green dot are much closer to the green dot. Hence, if anything, the average will be to the left of the green dot, not to its right.”

Here we are visually using the concept of deviation to find the average. The average of some numbers lies somewhere in the middle of the numbers such that the distance of the smaller numbers from the average is the same as the distance of the greater numbers. To understand this, check out this post: http://www.veritasprep.com/blog/2012/05/quarter-wit-quarter-wisdom-finding-arithmetic-mean-using-deviations/

Here we are saying that the average will be around the green dot. The distance of the dots on left (which represent around 2.1 and 2.4 hrs) will be much more from the green dot (which represents about 5) than the distance of the dots on the right (which represent 5.8, 6.4 and 7.3) from the green dot. Hence the average will be skewed towards left of the green dot. It’s the deviation concept being used visually.

Hi Karishma,

For the second question, I wasted a ton of time on calculating (by approximation) the averages of all the 3 sets and ended up with really close together answer choices and could not pick one over the other because of poorly and quickly approximating.

Although I do like your visual approach to finding the average, I still do not get how you chose to place those dots in those specific spots and especially their position relative to each other. You are also approximating at some level but seem sure of their placement somehow. Am I missing something critical here?