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The histogram shows the frequency distribution of the number of calls serviced by a call centre in a day by duration (in minutes) of the calls. Introduction of a new methodology will decrease the mean call time by 20%. What will the mean call time be after the new methodology is introduced?  

The histogram shows the frequency distribution of the number of calls serviced by a call centre in a day by duration (in minutes) of the calls. Introduction of a new methodology will decrease the mean call time by 20%. What will the mean call time be after the new methodology is introduced?   Correct Answer 2.64 min

Calculation:

From the figure, 

Mean = (x1y1 + x2y2 + ..... + x6y6)/Sum of frequency 

x1 , x2 , x3 ... are number of calls and y1 , y2 , y3 ..... is the average of the duration of the call

y1 = (0 + 1)/2 = 0.5 

Similarly

y2 = 1.5, y3 = 2.5, y4 = 3.5, y5 = 4.5, y6 = 5.5, 

Actual mean in day = (100 × 0.5 + 200 × 1.5 + 300 × 2.5 + 400 × 3.5 + 300 × 4.5 + 200 × 5.5)/(100 + 200 + 300 + 400 + 300 + 200)

⇒ Actual mean in day = 4950/1500

⇒ 3.3 minutes

After new methodology , 20% reduced 

So, New mean = 3.3 × 80/100 = 2.64 minutes

New mean in minutes = 2.64 minutes  

∴ The required answer is 2.64 minutes 

Note:- Values of the actual exam may differ

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