Analyzing Production Data from the Table

The question provides a table showing the production quantities for five different companies (P, Q, R, S, and T) across two different years (L and M). We need to carefully examine this table and evaluate two statements based on the data to determine which statement is incorrect.

Analyzing Statement I: Average Production in Year L

Statement I claims that the average production of companies P, Q, R, and S in year L is 172.5. To verify this, we need to calculate the average production for these companies in year L using the data from the table.

Production in Year L for P, Q, R, and S are:

• P: 150
• Q: 190
• R: 130
• S: 180

To find the average, we sum the production values and divide by the number of companies (which is 4):

\text{Average Production (P, Q, R, S in Year L)} = \frac{\text{Sum of Production}}{\text{Number of Companies}}

\text{Average Production} = \frac{150 + 190 + 130 + 180}{4}

Let's calculate the sum:

150 + 190 = 340

340 + 130 = 470

470 + 180 = 650

Now, divide the sum by 4:

\text{Average Production} = \frac{650}{4}

\frac{650}{4} = 162.5

Our calculated average production is 162.5. Statement I says the average is 172.5. Since 162.5 is not equal to 172.5, Statement I is incorrect.

Analyzing Statement II: Ratio of Production for Company T

Statement II claims that the ratio of production of company T in year L to the production of company T in year M is 6 ∶ 7.

From the table, we find the production values for Company T:

• Production of T in Year L: 120
• Production of T in Year M: 140

The ratio of production of T in year L to year M is written as:

\text{Ratio} = \text{Production in Year L} : \text{Production in Year M}

\text{Ratio} = 120 : 140

To simplify this ratio, we need to find the greatest common divisor (GCD) of 120 and 140 and divide both numbers by it. The GCD of 120 and 140 is 20.

\frac{120}{20} = 6

\frac{140}{20} = 7

So, the simplified ratio is 6 : 7.

Our calculated ratio is 6:7. Statement II says the ratio is 6 ∶ 7. Since our calculated ratio matches the statement, Statement II is correct.

Conclusion: Identifying the Incorrect Statement

Based on our analysis:

• Statement I: The average production of P, Q, R, and S in year L is 162.5, which does not match 172.5. So, Statement I is incorrect.
• Statement II: The ratio of production of T in year L to year M is 120:140, which simplifies to 6:7. This matches the statement. So, Statement II is correct.

The question asks which of the following statements is NOT correct. Only Statement I is not correct.

Revision Table: Key Calculations Reviewed

Here is a quick look at the calculations performed:

Additional Information: Understanding Average and Ratio

Average: The average (or arithmetic mean) of a set of numbers is found by summing all the numbers in the set and then dividing the sum by the count of numbers in the set. It gives a central value for the set of numbers.

\text{Average} = \frac{\text{Sum of values}}{\text{Count of values}}

Ratio: A ratio is a comparison of two quantities. It shows how many times one quantity is contained within another. Ratios can be written with a colon (a:b), as a fraction (\(\frac{a}{b}\)), or using the word "to" (a to b). Ratios are often simplified to their lowest terms by dividing both parts by their greatest common divisor.

For example, the ratio 120:140 simplifies to 6:7 because both 120 and 140 are divisible by 20.

Understanding how to calculate averages and simplify ratios is crucial for solving data interpretation problems like this one.