50 student's exam marks out of 100 are reported below in bar chart

Question

50 students' exam marks out of 100 are reported below in bar chart. The result is summarised as follows: 8 students attained less than 10 marks, another 8 students attained at least 10 , but less than 20 marks and so on. https://gmatclub.com/forum/download/file.php?id=89011 Based on the given information use the drop down menus to most accurately complete the following statements. A. The least possible value of mean marks for the whole class of 50 students would be GRAPH_1_PLACEHOLDER B. Maximum possible no. of students attaining marks in the range of (20-46) would be GRAPH_2_PLACEHOLDER GMAT-Club-Forum-2gzs3ora.png

ankushsambare · Answer

Here's the solution in simple text:
 A. Finding the Least Value 
Multiply each bar value by the corresponding left-side frequency:
8 × 0 = 0
10 × 8 = 80
20 × 7 = 140
30 × 6 = 180
40 × 6 = 240
70 × 7 = 490
80 × 5 = 400
90 × 3 = 270
Total value = 80 + 140 + 180 + 240 + 490 + 400 + 270 = 1800
Total frequency = 50
Least value = 1800 ÷ 50 = 36
 Answer: 36

B. Finding the Maximum Value 
Take the complete bar value for the interval 40–50.
Total frequency = 7 + 6 + 6 = 19
 Answer: 19

kingbucky · Answer

least possible value  of mean marks for the whole class of 50 students would be :

Consider all the lower bounds and take the average. It comes to 36.

8 × 0 + 10 × 8 + 20 × 7 + 30 × 6 + 40 × 6 + 70 × 7 + 80 × 5 + 90 × 3 = 1800
1800/50= 36

B.  Maximum possible no. of students attaining marks  in the range of (20-46) would be

Here we add the count from :
 19

Edskore · Answer

This is a good example of why Data Insights loves grouped data, the trick is always about what you don't know within each bucket.

1. From the chart: [0,10) has 8 students, [10,20) has 8, [20,30) has 7, [30,40) has 6, [40,50) has 6, [70,80) has 7, [80,90) has 5, [90,100) has 3. That's 50 total, checks out.
2. For the least possible mean: since each interval includes its lower bound but not its upper one, the smallest a student in a bucket could have scored is the left edge. To minimize the mean, assume everyone scored the floor of their bucket.
3. Multiply each lower bound by its frequency and sum: 0x8+10x8+20x7+30x6+40x6+70x7+80x5+90x3 = 1800. Divide by 50: mean = 36.
4. For max students in the range 20 to 46: the full [20,30) and [30,40) buckets sit entirely inside that range, that's 7+6=13. The [40,50) bucket goes up to just under 50, so all 6 students there could still land at or below 46. Total = 7+6+6 = 19.

Both parts trip people up the same way, forgetting that a grouped interval is a range, not one number, and GMAT wants the extreme values inside it, not the midpoint.

One-liner: with bucketed data, always ask what's the most extreme value hiding inside each bucket before you average or count anything.

50 student's exam marks out of 100 are reported below in bar chart

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