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The following data represent the monthly phone use, in minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. what is the cutoff point?321 474 461 548406 464 517 311534 425 377 505322 435 410 513499 354 307 363The cutoff point is ____minutes( round to the nearest minute)

Sagot :

Answer:

The answer is "717.25 minutes".

Step-by-step explanation:

In this question first, we arrange the value in ascending order that are:

307,311,321,322,354,363,377,406,425,435,461,464,474,499,505,513,517,534,548

The median is always in an orderly position that is [tex]= \frac{(n+1)}{2}[/tex].

[tex]\to \frac{(n+1)}{2} = \frac{(20+1)}{2} = 10.5[/tex]  position orders

[tex]10^{th} \ and \ 11^{th}[/tex] place an average of observations so, the

[tex]Average = \frac{(425 +435)}{2} = \frac{(860)}{2} =430[/tex]

Because as medium stands at 10.5 that median is as below 10 are greater than the level.

[tex]Q_1[/tex] often falls throughout the ordered BELOW average is [tex]= \frac{(n+1)}{2}[/tex] place.

[tex]\to \frac{(n+1)}{2} = \frac{(10+1)}{2} = 5.5^{th}[/tex]ordered position

Average [tex]5^{th} \ and \ 6^{th}[/tex]  location findings

[tex]Q_1 = \frac{(354+363)}{2} = \frac{(717)}{2}= 358.5[/tex]

In  [tex]= \frac{(n+1)}{2}[/tex] the ordered place, Q3 always falls ABOVE the median.

[tex]\to \frac{(n+1)}{2} = \frac{(10+1)}{2} = 5.5^{th}[/tex] ordered At median ABOVE 

Consequently [tex]Q_3[/tex] falls between [tex]5^{th} \ and \ 6^{th}[/tex] ABOVE the median position

[tex]15^{th}\ and \ 16^{th}[/tex]place average of observations

[tex]\to Q_3 = \frac{(499+505)}{2}=\frac{(1004)}{2} = 502[/tex]

[tex]\to IQR = Q_3 - Q_1= 502-358.5= 143.5[/tex]  

[tex]\to \text{Upper fence} = Q_3 + 1.5 \times IQR= 502 + 1.5 \times 143.5 = 717.25[/tex]

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