Understanding the Data Distribution

The question provides a table showing the percentage distribution of teachers across six universities (A, B, C, D, E, F). We are also given the exact number of teachers in University E, which is 1856. This information is key to finding the total number of teachers across all universities.

We are asked to find the difference (M-L), where L is the total number of teachers in Universities A, B, and C, and M is the total number of teachers in Universities D, E, and F. Finally, we need to identify which university has a number of teachers equal to this difference (M-L).

Calculating the Total Number of Teachers

The total number of teachers in University E is 1856, which represents 29% of the total teachers across all six universities. We can use this to find the total number of teachers.

Let the total number of teachers be $T$.

According to the data:

$\text{29% of } T = 1856$

$\frac{29}{100} \times T = 1856$

$T = \frac{1856 \times 100}{29}$

$T = 64 \times 100$

$T = 6400$

So, the total number of teachers in all six universities is 6400.

Calculating Teachers in Each University

Now we can calculate the number of teachers in each university using their respective percentages and the total number of teachers (6400).

• Teachers in A = 11% of 6400 = $\frac{11}{100} \times 6400 = 11 \times 64 = 704$
• Teachers in B = 17% of 6400 = $\frac{17}{100} \times 6400 = 17 \times 64 = 1088$
• Teachers in C = 19% of 6400 = $\frac{19}{100} \times 6400 = 19 \times 64 = 1216$
• Teachers in D = 6% of 6400 = $\frac{6}{100} \times 6400 = 6 \times 64 = 384$
• Teachers in E = 29% of 6400 = $\frac{29}{100} \times 6400 = 29 \times 64 = 1856$ (Matches given data)
• Teachers in F = 18% of 6400 = $\frac{18}{100} \times 6400 = 18 \times 64 = 1152$

Let's verify the total: $704 + 1088 + 1216 + 384 + 1856 + 1152 = 6400$. The individual calculations are correct.

Calculating L and M

L is the total number of teachers in Universities A, B, and C:

$L = \text{Teachers in A} + \text{Teachers in B} + \text{Teachers in C}$

$L = 704 + 1088 + 1216 = 3008$

M is the total number of teachers in Universities D, E, and F:

$M = \text{Teachers in D} + \text{Teachers in E} + \text{Teachers in F}$

$M = 384 + 1856 + 1152 = 3392$

Calculating M - L

Now, we find the difference M - L:

$M - L = 3392 - 3008$

$M - L = 384$

Identifying the University with M - L Teachers

We need to compare the value of M - L (384) with the number of teachers in each university:

• Teachers in A: 704
• Teachers in B: 1088
• Teachers in C: 1216
• Teachers in D: 384
• Teachers in E: 1856
• Teachers in F: 1152

The number of teachers equal to M - L (384) is found in University D.

Summary of Calculations

The value of M - L is 384, which is exactly the number of teachers in University D.

Revision Table: Data Interpretation Practice

Additional Information: Data Interpretation Skills

Data interpretation questions often involve tables, charts, or graphs that represent data. The key skills required to solve such problems include:

• Reading and Understanding Data: Carefully reading the table or chart to understand what the data represents and the units used.
• Calculating Percentages: Understanding how to calculate percentages, percentage increases/decreases, and how to find a value given a percentage of a total.
• Calculating Ratios and Proportions: Comparing quantities using ratios and solving for unknown values using proportions.
• Averages: Calculating the average of a set of values.
• Addition and Subtraction: Summing up values or finding the difference between them, as done in this problem to calculate L, M, and M-L.
• Comparing Values: Comparing calculated values to determine relationships or find matches, as done here to find which university's teacher count equals M-L.

Practicing with different types of data representation (tables, bar graphs, pie charts, line graphs) helps improve data interpretation skills for exams.