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 What is the total number of students whose height is less than or equal to 165 cm?
B. 39
The cumulative frequencies for the given class intervals are calculated as follows: Height 162 cm: 12 Height 164 cm: 12 + 15 = 27 Height 166 cm: 27 + 24 = 51 To find the number of students with height less than or equal to 165 cm, we use linear interpolation within the class interval 164–166. The number of students in the interval 164–166 is 24. Assuming a uniform distribution of frequencies within the class interval, the number of students with height between 164 cm and 165 cm is: 165 - 164 166 - 164 24 = 1 2 24 = 12 The total number of students whose height is less than or equal to 165 cm is the sum of students with height 164 cm and those between 164 cm and 165 cm: 27 + 12 = 39 Answer: 39
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