Question

A survey of $200$ people was conducted who rated two of the movies watched in the theater. Their feedback was collected and presented in a joint relative frequency table as given below.
Identify the incorrect statement about the data from the following:

• A. $120$ people gave less than 5 stars.
• B. $60$ people who watched movie B gave less than $5$ stars.
• C. $43$% of people watched movie A.
• D. Movie B gets more $5$ stars than movie A.

Answer 1

The correct option is A $120$ people gave less than 5 stars.

Let us analyze the options one by one using the joint relative frequency table.

Option A:
A joint relative frequency is the ratio of the frequency in a particular category and the total number of data values,

i.e., Joint relative frequency of the given category $=\frac{\text{Frequency in that category}}{\text{Total number of data values}}$

Joint relative frequency of people who watched movie B and gave less than $5$ stars $=\frac{\text{Number of people who watched movie B and gave less than 5 stars}}{\text{Total number of people}}$

$\Rightarrow 0.30=\frac{\text{Number of people who watched movie B and gave less than 5 stars}}{200}$

$\Rightarrow$ Number of people who watched movie B and gave less than $5$ starts $=0.30\times 200$
$=60$
$\Rightarrow$ Option A is correct.

Option B:
A marginal relative frequency is the sum of the joint relative frequencies in a row or a column.
Marginal relative frequency of people who watched Movie A $=0.15+0.28$
$=0.43$ or $43$%
$=$ Percentage of people who watched movie A
$\Rightarrow$ Option B is correct.

Option C:
Using the relative frequency table, we have
Joint relative frequency of people who watched movie A and gave $5$ stars $=0.15$
Joint relative frequency of people who watched movie B and gave $5$ stars $=0.27$
$\Rightarrow$ Movie B gets more $5$ stars than movie A
$\Rightarrow$ Option C is correct.

Option D:
Using the table we have,
Marginal relative frequency of people who have less than $5$ stars $=0.58$
$\Rightarrow$ Number of people who gave less than $5$ stars $=0.58\times$ Total number of people
$=0.58\times 200$
$=116\ne 120$
$\Rightarrow$ Option D is incorrect.