Question

The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy or New York, New York.
Maximum Minimum Q1 Q3 IQR Median Mean σ
Rome 16 0 3 13 10 8.5 8 5.4
New York 20 1 4.5 6 1.5 5.5 7.25 6.1

Which of the choices below best describes how to measure the center of this data?

Both centers are best described with the median.

The Rome data center is best described by the mean. The New York data center is best described by the median.

The Rome data center is best described by the median. The New York data center is best described by the mean.

Answer 1

Solution:

1. Rome

Minimum=0

Maximum=16

$Q_{1}=3, Q_{3}=13, {\text{IQR}=Q_{3}-Q_{1}=13-3=10,$

Median ,$Q_{2}=8.5$

Mean = 8

Standard Deviation(σ)=5.4

As, difference between , Maximum -Mean =Mean - Minimum=8

So, Mean will Worthy description to find the center of Data set, given about Rome.

2. New York

Minimum=1

Maximum=20

$Q_{1}=4.5, Q_{3}=6, {\text{IQR}=Q_{3}-Q_{1}=6-4.5=1.5,$

Median ,$Q_{2}=5.5$

Mean = 7.25

Standard Deviation(σ)=6.1

As, for New york , Mean is not the mid value, that is difference between Mean and Minimum is not same as Maximum and Mean.

As, you can see , the three Quartiles , $Q_{1},Q_{2},Q_{3}$ are very close to each other, it means , other data values are quite apart from each other. So, Mean will not  appropriately describe the given data.So, in this case Median will suitable to find the center.

Option (B): The Rome data center is best described by the mean. The New York data center is best described by the median.