Question

USH Financial is examining the use of its midtown ATM machine. The numbers of transactions made per day at this ATM during the past 20 days are as follows.

Answer 1

Given the data of the problem, we must answer some questions.

(a) In this problem all the central tendency measures can be computed.

(b) We answer this question by computing the mean, median and mode.

1) For the original set of values, we have:

• The ,mean, is given by the sum of all the data divided by the number of values:

`(1505)/(20)=75.25.`

• The ,median, is the data value separating the upper half of a data set from the lower half.

`51,59,63,64,66,68,74,74,74,(74,75),77,77,79,82,84,86,88,91,99.`

The values 74 and 75 are the values in the middle of the list, the median is the mean of these values:

`(74+75)/(2)=74.5.`

• The ,mode, is the value or values in the data set that occurs most frequently:

`74.`

2) For the new set of values, we have:

• The ,mean,:

`(1464)/(20)=73.2.`

• The ,median, takes the same value because if we change the first value of the list, the values (74,75) will remain in the center, and the median will be again 74.5.

,

• The ,mode ,takes the same value because the number 74 will be again the most repeated value in the list.

(c) If we remove the last value of the list, the new measures of central tendency will be:

• The mean is:

`(1480)/(20)=74.`

• The median is 74 now, because the central value is 74:

`51,59,63,64,66,68,74,74,74,(74),75,77,77,79,82,84,86,88,91`

• The mode is still 74 because the number 74 remains the most repeated value.

Answers

(a) All of these measures exist.

(b) Mean.

(c) Mean and median.