Consider the following for the four (04) items that follow: The frequency distribution of height of students of a class is given below: Height (in cm) Number of Students 160–162 12 162–164 15 164–166 24 166–168 13 The height which occurs most frequently in the class is
D. 164.9 cm
The height which occurs most frequently corresponds to the mode of the given frequency distribution. The maximum frequency is 24, which corresponds to the class interval 164-166. Thus, the modal class is 164-166. The lower limit of the modal class, l = 164 Frequency of the modal class, f_1 = 24 Frequency of the class preceding the modal class, f_0 = 15 Frequency of the class succeeding the modal class, f_2 = 13 Class size, h = 2 The mode is calculated using the formula: Mode = l + ( f_1 - f_0 2f_1 - f_0 - f_2 ) h Substituting the values: Mode = 164 + ( 24 - 15 2(24) - 15 - 13 ) 2 Mode = 164 + ( 9 48 - 28 ) 2 Mode = 164 + ( 9 20 ) 2 Mode = 164 + 9 10 = 164 + 0.9 = 164.9 The height which occurs most frequently is 164.9 cm. Answer: 164.9 cm
Related: Mathematics — Statistics · All PYQ Banks