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In the following frequency distribution Height (in cm) 140–145 145–150 150–155 155–160 160–165 165–170 No. of students 13 15 9
Question

In the following frequency distribution

Height (in cm)

140–145

145–150

150–155

155–160

160–165

165–170

No. of students

13

15

9

10

8

5

The sum of the upper limit of the modal class and the lower limit of the median class:

A.

310

B.

295

C.

305

D.

300

Correct option is D

Solution:
Identify the Modal Class
Modal class = class with highest frequency
Frequencies: 13, 15, 9, 10, 8, 5
Highest frequency = 15 => Modal class = 145–150
Upper limit of modal class = 150
Identify the Median Class
Total number of students =
13+15+9+10+8+5=60
Median lies at the 602=30thitem \frac{60}{2} = 30^{th} item​​
Compute cumulative frequency:
  • Up to 140–145: 13
  • Up to 145–150: 13 + 15 = 28
  • Up to 150–155: 28 + 9 = 37
30th item lies in class 150–155
Lower limit of median class = 150
Add required limits
Upper limit of modal class = 150
Lower limit of median class = 150
Sum = 150 + 150 = 300
Correct answer is (d) 300

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