Question

Use the table given below to find fhe following:

Class interval	30−34	35−39	40−44	45−49	50−54	55−59
Frequency	7	10	12	13	8	4

(A) The size of the third class.

(B) The class mark of the third class.

(C) The class boundaries of the sixth class.

(D) The actual class limits of the fourth class.

(E)The upper and lower limits of the fifth class.

Answer 1

STEP 1 : The size of the third class.

The size of the class is the difference between the lower and upper limit

The size of the third class$$\begin{gathered} =44-40 \\ =4 \end{gathered}$$

So, The size of the third class is $4$.

STEP 2 : The class mark of the third class.

Class mark, in statistics, is the average of the upper limit and the lower limit of a class in a frequency distribution.

The class mark of the third class $40-44$ is

$$\begin{gathered} =\frac{40+44}{2} \\ =\frac{84}{2} \\ =42 \end{gathered}$$

So, The class mark of the third class is $42$.

STEP 3 : The class boundaries of the sixth class.

Class boundary is the midpoint of the upper class limit of one class and the lower class limit of the subsequent class.

The class boundaries of the sixth class are:

$55–54=1$

Now,$\frac{1}{2}=0.5$

$54+0.5=54.5$

$59+0.5=59.5$

So,The class boundaries of the sixth class are $54.5,59.5$

STEP 4 : The actual class limits of the fourth class.

The class limit of fourth class is $45-49$ are :

$45$ is the lower limit and $49$ is the upper limit.

STEP 5 :The upper and lower limits of the fifth class.

The upper limit of the fifth class is $54$

The lower limit of the fifth class is $50$.

Hence,

The size of the third class is $4$.

The class mark of the third class is $42$.

The class boundaries of the sixth class are $54.5,59.5$.

The actual class limits of the fourth class are $45,49$.

The upper and lower limits of the fifth class are $54,50$ respectively.