Answer to Question #206894 in Statistics and Probability for tony

Question

Shown here are four frequency distributions. Each is incorrectly constructed. State the

reason why.

Answer 1

The class widths of the frequency distribution are the difference between upper limit and lower limit of the classes. The width of the classes must be equal. The class width has some rules such as:

(i) The class widths of all the classes must be equal that is, must be uniform.

(ii) The class widths must be continuous, that is, the class boundaries have one additional value.

(iii) The class widths must not overlapped, that is, the upper limit of one class and lower limit of next class must not be same, due to this, data value is counted in both the classes.

a.

$$32-27=38-33=44-39=55-50=5$$

$$49-45=4\not=5$$

b.

$$9-5=13-9=17-13=24-20=4$$

$$20-17=3\not=4$$

c.

The class widths must be continuous, that is, the class boundaries have one additional value.

Possible classes: $123-127, 128-132, 133-137, 138-142,143-147$

We see that the class $133-137$ is absent.

d.

$$13-9=4, 19-14-5, 25-20=5, 28-26=2,$$

$$28-26=2,32-29=3$$

The class widths of all the classes must be equal that is, must be uniform.