Math Problem Statement

use a graph to solve A retail company wants to explore the relationship between the amount of time employees spend interacting with customers (measured in hours per week) and their total sales revenue (measured in thousands of rupees per month). The company collects data from 10 randomly selected employees and records their weekly customer interaction hours and monthly sales revenue as follows: Employee Interaction Hours Sales Revenue (Rs. ‘000s) 1 5 110 2 10 125 3 15 185 4 20 255 5 25 257 6 30 246 7 35 286 8 40 280 9 45 315 10 50 320 a. Plot the above data on a graph paper and interpret the relationship you can observe.

Solution

The graph above shows the relationship between the number of hours employees spend interacting with customers and their corresponding sales revenue (in thousands of rupees). From the plot:

  1. Positive correlation: There is a generally positive trend, as increased customer interaction hours seem to be associated with higher sales revenue. The trendline, though not perfectly fitting all points, shows that on average, sales revenue increases as interaction hours increase.

  2. Trendline equation: The equation of the trendline is y=4.50x+111.5y = 4.50x + 111.5, which suggests that for every additional hour spent interacting with customers, the sales revenue increases by approximately 4.5 thousand rupees.

  3. Saturation point: Around 25-30 interaction hours per week, the sales revenue growth slows down, indicating that after a certain point, additional interaction hours may not lead to significant increases in sales revenue. Some data points, such as at 25 and 30 hours, show a flattening or slight decrease.

Would you like more details or have any questions about the analysis?

Here are 5 related questions:

  1. What other factors might affect sales revenue besides interaction hours?
  2. Could a non-linear model fit the data better?
  3. How can the company use this information to improve employee performance?
  4. What might explain the slight dip in sales after 30 interaction hours?
  5. Would a larger dataset provide a more accurate analysis?

Tip: When modeling real-world data, exploring different types of trendlines (e.g., quadratic) might reveal more nuanced relationships.

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Correlation
Scatter Plot

Formulas

y = mx + b (Linear Equation)

Theorems

Correlation Coefficient
Linear Regression Theorem

Suitable Grade Level

Grades 10-12