The designers of a video game hired 100 game testers to play the game

Question

The designers of a video game hired 100 game testers to play the game to determine whether the level of difficulty was appropriate. Each of the 100 testers made at most 25 attempts to complete each of the game's 15 levels (Levels 1–15). When a tester completed a level, he or she then made no further attempts at that level. For each of the levels, the table shows, among the testers who completed the level, the total number of testers whose number of attempts to complete that level fell in various ranges.

Number of attempts      Level    1 to 5    6 to 10    11 to 15    16 to 20    21 to 25    Total completed      1  26  28  15  2  0  71    2  91  8  1  0  0  100    3  65  13  9  2  2  91    4  73  17  5  3  1  99    5  33  22  6  7  1  69    6  95  5  0  0  0  100    7  62  14  10  8  3  97    8  82  15  2  0  0  99    9  13  17  11  5  3  49    10  2  7  6  3  1  19    11  51  9  8  8  1  77    12  9  5  8  2  6  30    13  20  13  10  7  5  55    14  0  0  3  2  4  9    15  8  12  6  8  4  38

For each of the following statistical measures, select  Must be 20 or less  for every level if, based on the information provided, the measure must be at most 20 for each of the 15 levels. Otherwise, select  Could be greater than 20  for one or more.

ID: 700255

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chetan2u · Accepted Answer

We are looking at details of attempts taken to finish each of the 15 level by 100 of the game testers.

For each of the following statistical measures, select Must be 20 or less for every level if, based on the information provided, the measure must be at most 20 for each of the 15 levels. Otherwise, select Could be greater than 20 for one or more.

So, we have to mainly concentrate on the tab of 20-25 and work on the extreme cases on the higher side.

1. Mean of the total number of attempts to complete for all testers who completed the level.

Check if any of the levels has more number of attempts in 15-20 and 20-25 attempts than the sum of all other columns.
When you scan the table, the level 14 stands out as there are 3 in 11-15 attempts , 2 in 16-20 attempts and 4 in 21-25 attempts.
 So, the max mean would be when all the testers took the maximum attempt in each case, so 3 took 15 attempts, 2 took 20 attempts and 4 took 25 attempts. 
Mean = \frac{ 3*15+2*20+4*25}{3+2+4} = \frac{185}{9}  = 20.xy >20.... Could be greater than 20.

2. Median of the total number of attempts to complete for all testers who completed the level

Check if any of the levels has more number of attempts in 20-25 attempts than the sum of all other columns.
 When you scan the table, no level has sum of numbers under 1-5, 6-10, 11-15 and 16-20 attempts less than that under 21-25. 
Thus median will always be 20 or less......  Equal to or less than 20

3. Range of the total number of attempts to complete for all testers who completed the level

If any level has been finished be some tester in 1-5 attempts while there are some more who have finished it in 20-25 attempts, the maximum range could be 25-1 = 24. 
There are many under this case: Level 3, 4, 5, 7, 9-15
  Could be greater than 20

darthvader20 , check the second case an dsee if that settles your query.

KarishmaB · Answer

This is what the table tells us: It gives info on each of the 15 levels of the game. Say take level 10. 2 people cleared it in 1 to 5 attempts, 7 people in 6 to 10 attempts etc. ... So if I were to write down the number of attempts of everyone who cleared the level 10 in increasing order, it could look something like this: 1, 3, 6, 6, 7, 8, 9, 9, 10, 11 ... etc. Question 1. Mean of the total number of attempts to complete for all testers who completed the level For every level, should the "Mean of the total number of attempts to complete for all testers who completed the level" be upto 20 or can it be more than 20 too? Sort the table by 21-25 attempts. Very few people lie in the 21-25 range. Sort the table by "Total Completed". For level 14, 9 total people completed and 4 of them took 21 - 25 attempts. Can the mean be above 20 here? To maximize the attempts, assume that 3 people took 15 attempts each, 2 people took 20 attempts each and 4 people took 25 attempts each. By the concept of deviation, we see immediately that mean here will be more than 20. Hence, here the mean CAN be above 20 in a case. It is not necessary that it m ust be 20 or less. SELECT: Could be greater than Question 2. Median of the total number of attempts to complete for all testers who completed the level The median will be the number of attempts of the middle person. Sort by "Total Completed" For level 14, there are 5 people who took 20 or fewer attempts. So the 5th person (middle person) took 20 or fewer attempts only. So the median will be 20 or less. For all other levels, the middle person is certainly at 20 or fewer attempts because 21-25 have very few people compared with the total number of people who completed the level. Hence median must be 20 or less for each level. We cannot say what the median will be, we only know it will be 20 or less. Select: Must be 20 or less Quetsion 3. Range of the total number of attempts to complete for all testers who completed the level The range for all testers could be greater than 20 for most levels. Level 10 has 2 people in 1-5 (say both took 1 attempt each) and 1 in 21 - 25 (say he took 25 attempts). So the range here will be 24, i.e. more than 20. Hence a range of more than 20 is certainly possible. SELECT: Could be greater than Table Analysis discussed here: https://youtu.be/41uPmg6ipos

darthvader20 · Answer

The question is from the official DI OG online question bank

Attaching the snippets of the questions and the table

Sans8 · Answer

Here are my 2 cents!

In first attempt qstn looks quite complicated, but if we're well verse with the concepts of average it is easy.

Starting with Qstn stem :   For each of the following statistical measures,   select Must be 20 or less     for every level     if, based on the information provided, the measure   must be at most 20     for each of the 15 levels      .     Otherwise, select Could be greater than 20 for one or more.

So necessarily, we need to select must be 20 or less if for EVERY LEVEL the solution comes out to be less than equal to 20, otherwise select could be.

Q1:   Mean of the total number of attempts to complete for all testers who completed the level

For every level the average of total number of attempts should be less than equal to 20 for must be true option.
Now,
Since we know from weighted average concept that avg shifts towards the higher weight.
Hence, on scanning the table almost all levels have very high weights in the range of 1-15 attempts.
But, 
Level 14 has weight of 3 in 11-15, 2 in 16-20, and 4 in 21-25.
Taking the worst case scenario all 3 took 15 attempts, all 2 took 20 attempts and 4 took 25 attempts
Therefore,
3*15+2*20+4*25/9 which comes out to be greater than 20.
Hence   could be greater than 20.

Q2:  Median of the total number of attempts to complete for all testers who completed the level
   All the majority or 50th percentile attempt lies in less than 20 attempts. Hence,   must be less than 20  .

Q3:  Range of the total number of attempts to complete for all testers who completed the level

Participant except 1,2,6 and 8 has their attempts lying in 21-25 and 1-5 range
Hence all have max possible range of more than 20.
Therefore,   Could be greater than 20

Hope that makes sense!!

onlymalapink · Answer

solved this question in under 2 mins and have no idea what the solutions are doing I jut took the means as the middle is the 3rd and for median around the same

just sort the 3rd tab

The designers of a video game hired 100 game testers to play the game

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Level	1 to 5	6 to 10	11 to 15	16 to 20	21 to 25	Total completed
	Number of attempts
1	26	28	15	2	0	71
2	91	8	1	0	0	100
3	65	13	9	2	2	91
4	73	17	5	3	1	99
5	33	22	6	7	1	69
6	95	5	0	0	0	100
7	62	14	10	8	3	97
8	82	15	2	0	0	99
9	13	17	11	5	3	49
10	2	7	6	3	1	19
11	51	9	8	8	1	77
12	9	5	8	2	6	30
13	20	13	10	7	5	55
14	0	0	3	2	4	9
15	8	12	6	8	4	38

Must be 20 or less	Could be greater than
		Mean of the total number of attempts to complete for all testers who completed the level
		Median of the total number of attempts to complete for all testers who completed the level
		Range of the total number of attempts to complete for all testers who completed the level

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The designers of a video game hired 100 game testers to play the game