Q.


The heights of 50 students, measured to the nearest centimeters, have been found to
be as follows

161   150   154   165   168   161   154   162   150    151
 


162   164   171   165   158   154   156   172   160   170
 


153   159  161   170   162   165   166   168   165    164
 


154   152  153   156   158   162   160   161    173   166
 


161   159   162   167   168   159   158   153   154   159


Which of the following options is correct for the given data?
 


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a

50% of the students are shorter than 165 cm.

b

50% of the students are higher than 165 cm.

c

50% of the students are shorter than 155 cm.

d

50% of the students are higher than 155 cm.  

answer is A.

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Detailed Solution

Given data,
161   150   154   165   168   161   154   162   150    151
 162   164   171   165   158   154   156   172   160   170
 153   159  161   170   162   165   166   168   165    164
 154   152  153   156   158   162   160   161    173   166
 161   159   162   167   168   159   158   153   154   159
The maximum and minimum height ranges of the pupils are also included in this table, along with information on which range the majority of the students fall in.
50 students make up the class as a whole.
The height range for a student in the class is between 150 and 155.
The height of a pupil in the class may not exceed 170 to 175 inches.
To determine the range in which the majority of students fall:
Students that are under 165 cm,
12 + 9 + 14
  35
Percentage,
%= 35 50 ×100     %=70%
Therefore, it can be inferred from the following table that the minimum range of heights is 150–155 and the maximum range is 170–175 inches.
Additionally, it can be inferred from the data that more than 50% of the kids are under 165 cm in height.
Therefore the answer is option (1).
 
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