Question

Refer to the following information from a frequency distribution for "heights of college women" recorded to the nearest inch:The first two class midpoints are 62.5" and 65.5".What are the class limits for the lowest class? A. 61 and up to 64B. 62 and up to 64C. 62 and 65D. 62 and 63

Answer 1

Answer: Therefore, Option 'A' is correct.

Explanation:

Since we have given that

Two class midpoints are 62.5 and 65.5

So, the class interval would be

`65.5-62.5=3`

So, the limits of lower class are
`x_1\ and\ x_2`

The limits of upper class are
`x_2\ and\ x_3`

So, it becomes,

`(x_1+x_2)/(2)=62.5\\\\x_1+x_2=62.5* 2=125`

and

`(x_2+x_3)/(2)=65.5\\\\x_2+x_3=65.5* 2=131`

Since we have given that interval is 3.

So,
`x_2-x_1=3\ and\ x_3-x_2=3`

So, by solving all the questions, we get that

`x_2+x_1=125\\\\x_2-x_1=3\\\\-------------------------\\\\2x_2=128\\\\x_2=64\\\\x_2-x_1=3\\\\64-x_1=3\\\\x_1=61\\\\and\\\\x_3-x_2=3\\\\x_3-64=3\\\\x_3=67`

Hence, the class limits would be

(61,64) and (64,67).

And the class limits of lowest class are 61 and 64.

Therefore, Option 'A' is correct.