The questions that follow are based on the following information. Following is the frequency distribution of heights of students in 7th standard of a certain school.Height in cm Number of boys Number of girls 145 2 5 150 3 6 155 5 9 160 15 10 165 5 0 Total 30 30
Which of the following statements is true ?
The mode of the height of boys and that of girls are same.
The mode of a discrete frequency distribution is the value of the variable that has the highest frequency, that is, the height that occurs most often. To compare the modes, we only need to locate the largest frequency in the boys' column and in the girls' column of the table and read the corresponding height.
Boys: frequencies = 2, 3, 5, 15, 5
Highest frequency = 15, at height 160 cm
Mode of boys = 160 cm
Girls: frequencies = 5, 6, 9, 10, 0
Highest frequency = 10, at height 160 cm
Mode of girls = 160 cm
Difference = \(160 - 160 = 0\) cm
Both distributions peak at the same height of 160 cm, so the modes are equal. The statements claiming that the boys' mode is greater by 5 cm or by 0.5 cm, or smaller by 5 cm, all assume a non-zero difference and therefore do not agree with the table.
Hence, The mode of the height of boys and that of girls are same.
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