Question

The number of phone calls (in thousands) are made by a telephone company for five weeks as given below:

Week	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)
No. of Telephone calls	\(110\)	\(130\)	\(93\)	\(104\)	\(211\)

Taking a period of moving averages as 3 weeks, the graph of moving averages can be depicted directly as :

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is D

The problem requires calculating the moving average for a period of 3 weeks based on the given data. The moving average helps in smoothing out fluctuations and identifying trends.

Week	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)
Calls (in thousands)	\(110\)	\(130\)	\(93\)	\(104\)	\(211\)

Steps:

1. Calculate the 3-week moving averages:
   • Week 2-4:
     \( \text{Average} = \frac{110+130+93}{3} = \frac{333}{3} = 111\)
   • Week 3-5:
     \( \text{Average} = \frac{130+93+104}{3} = \frac{327}{3} = 109\)
   • Week 4-6:
     \( \text{Average} = \frac{93+104+211}{3} = \frac{408}{3} = 136\)

The moving averages for three periods are 111, 109, and 136 respectively. Based on these values, the correct graph is represented by the option with the average values plotted against their respective weeks, showing smoother fluctuation trends. The correct image option is the one reflecting these average points.