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Sajjad1994
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lets analyze this q :

we have 13 areas : now square is total 36 square units , so each side is 6 units and thus we have 36 squares with 1 unit sizes in this . Now lets find the areas of each different area coloured by observation : these come out to be

1,1,2,2,2,3,3,3,3,3,3,5,5 so we have mode = 3 , median = 3 , range = 5-1=4 and mean = 36/13 = 2.769

so the blanks fit in with only 2 items which is mode less than range by exactly 1


Measured in square units, the mode of the areas of the 13 colored regions is exactly___________than the_____________of those areas.

First Blank

answer is A. 1 less

A. 1 Less
B. 2 Less
C. 1 Greater
D. 2 Greater

Second Blank

answer is A. RANGE
A. Range
B. Mean
C. Median
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Measured in square units, the mode of the areas of the 13 colored regions is exactly___________than the_____________of those areas.

Total regions = 13
Total Area = 36
Orange Region areas - 2, 5, 1, 1, Total=9
Blue Region areas - 3, 3, 2 Total=8
White Region areas - 3, 3, 3, Total=9
Grey Region areas - 3, 2, 5, Total=10

All Regions (arranged) = 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 5, 5

Mean = \(\frac{36}{13}\) ~ 2.7
Median (7th val) = 3
Mode (highest count) = 3
Range (highest - lowest) = 5-1 = 4

We can see that the Mode (3) is exactly 1 less than the Range (4). So,

First Blank - A. 1 Less
Second Blank - A. Range
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As per the figure attached, we have area of Square = 36 square units, so one side length= 6 and it is equally distributed by dots.

So, distance between 2 dots = 1 unit

Area of 1 = 2*1 =2 square units,
Area of 2 = 1*1 =1 square unit,
Area of 3 = 2*1 +1*1 =3 square units,
Area of 4 = 2*1 +1*1 =3 square units,
Area of 5 = 1*1 =1 square unit,
Area of 6 = 2*1 +1*1 =3 square units,
Area of 7 = 3*1 +1*1 +1*1 =5 square units,
Area of 8 = 4*1 +1*1 =5 square units,
Area of 9 = 2*1 +1*1 =3 square units,
Area of 10 = 2*1 +1*1 =3 square units,
Area of 11 = 2*1 +1*1 =3 square units,
Area of 12 = 2*1 =2 square units,
Area of 13 = 2*1 =2 square units,

Now, in areas in ascending order: 1,1,2,2,2,3,3,3,3,3,3,5,5
mode = count of the most repeated integer = 6
Range = 5-1 = 4, Median = 3, Mean= (1+1+2+2+2+3+3+3+3+3+3+5+5)/13 = 36/13~3

Mode- Range = 6-4 = 2

Measured in square units, the mode of the areas of the 13 colored regions is exactly___________than the_____________of those areas.

1st blank: 2 units greater. D.
2nd blank: Range. A.
Attachments

Fig.PNG
Fig.PNG [ 118.81 KiB | Viewed 10569 times ]

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OA has been updated now its A for both blanks. Good work Sumi1010 and Deepakjhamb

I have feelings for you TarunKumar1234 you done a lot work but not in true direction :(

rocky620 I like it when you keep your post organized.

Official explanation will be posted soon have a look at that and match your answers and reasoning.

Thank you
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I saved some time by taking a structured approach to counting and organising the data sets to a tree and branch format:

1: II
2: III
3: IIIII I
4:
5: II

Therefore, mode is 3. Range is 5-4 = 4. Ans is "1 less" and "Range".
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