Question

Find the upper limit of the modal class from the given distribution.

Height [in cm] Number of girls
Below 140 4
Below 145 11
Below 150 29
Below 155 40
Below 160 46
Below 165 51

(a) 165
(b) 160
(c) 155
(d) 150

Answer 1

The modal class is the one with the highest frequency, which is from 145 cm to 150 cm. Therefore, the upper limit of the modal class is 150 cm.

Step-by-step explanation:

To find the upper limit of the modal class from the given distribution, we first need to determine which class interval has the highest frequency. The distribution provided is cumulative, meaning we need to calculate the frequency for each class by subtracting the cumulative frequency of the previous class from the current class.

For example: for the class interval 'Below 145', we subtract the frequency of 'Below 140' from it, and so on. The class with the largest frequency difference is the modal class. Once identified, we look at the upper boundary of that class to determine the upper limit of the modal class.

Let's calculate:

• 140 to 145 cm: 11 - 4 = 7 girls
• 145 to 150 cm: 29 - 11 = 18 girls (highest difference so far)
• 150 to 155 cm: 40 - 29 = 11 girls
• 155 to 160 cm: 46 - 40 = 6 girls
• 160 to 165 cm: 51 - 46 = 5 girls

Therefore, the modal class is from 145 cm to 150 cm and the answer is the upper limit of this class, which is 150 cm.