Question

4. The state funding agency wants to know the percentage of people in their study that have an income below the poverty line of $12,000. In an attempt to answer this question, the researchers from our main study provide a frequency distribution income in tabular form. Below is how they set up their table and plan to present it to the funding agency. (We don’t need the numbers for this table, but the incomes range from $0 to $100,000 with a mean of $22,000 and the median of $10,000.)

Frequency Distribution of Respondents

Interval	N	%
$1,000-$10,000
$10,000-$15,000
$15,0000 or more

4A. These research need serious help. What specific rules of constructing frequency distributions are they violating in the way they have set up their table?

4B. What other guidelines have that not followed well. Make two recommendations to revise the table that are not related to the violation of rules you identified in 4A. In other words, other than fixing the violated rules, what else would you recommend they fix.  

Answer 1

(4A)

Specific rules of constructing frequency distributions are they violating in the way they have set up their table:

(i) Number of classes:

Generally for a meaningful display, the number of classes is between 5 to 50. Here the number of classes isonly 3, which is very small. This will result into loss of data.

(ii) Range of Variable:

It is given that incomes range from $0 to $100,000. But in the Frequency Distribution, minimum value is 1000 and maximum value is 15,000 or more,. This is incorrect. The minimum value should be 0 andmaximum value should be 100,000.

(iii) Class Interval:

Generally it is got by dividing the range by number of classes. In the given frequency distribution, it has got varying class intervals. This is advisable only for specific situations.

(4B)

Other guidelines have that not followed well.

(i) It is noted from the given frequency distribution, the mean value of 22,000 liesin the last class, which is not desirable in respect of further analysis of data. The Frequency Table must beso constructed to have mean and median not on the tails.

(ii) It is noted that the state funding agency wants to know the percentage of people in their study that have an income below the poverty line of $12,000. So, while constructing the Frequency Distribution, if the value of 12,000 occurs at the end of one of the classes, we can find the required value easily.If it occurs in the middle ofthe class, the computations will become complex.