Question

Javier and Ercilia are supervisors at a shopping mall. Each was given the task of estimating the mean distance that shoppers live from the mall. They each randomly surveyed $100$shoppers. The samples yielded the following information.

a. How can you determine which survey was correct ?

b. Explain what the difference in the results of the surveys implies about the data.

c. If the two histograms depict the distribution of values for each supervisor, which one depicts Ercilia's sample? How do you know?

d. If the two box plots depict the distribution of values for each supervisor, which one depicts Ercilia’s sample? How do you know?

Use the following information to answer the next three exercises: We are interested in the number of years students in a particular elementary statistics class have lived in California. The information in the following table is from the entire section.

Short answer

(a) The sample variance gives the variability of the sample data. The survey with minimum variance is correct.

(b) Both the survey has same mean but different variance $\left(sd\right)$.

The variance can be used to determine the relation between the individual numbers with each other within a data set. In this, Javier's sample has more variability than Ercilia's sample.

(c) The histogram (b) is Ercilia's samples.

(d) Boxplot (b) shows Ercilia's samples.

Step-by-step solution

Survey : 

To create a map, plan, or description, examine and record the extent and features.

(a) Explanation :

Javier and Ercilia are supervisors at a shopping mall. Each of them was given the task of estimating the mean distance that shoppers live from the mall. They randomly surveyed $100$shoppers. The samples yield are,

The sample variance gives the variability of the sample data. The survey with minimum variance is correct.

(b) Explanation : 

Javier and Ercilia are supervisors at a shopping mall. Each of them was given the task of estimating the mean distance that shoppers live from the mall. They randomly surveyed $100$shoppers. The samples yield are,

Both the survey has same mean but different variance$\left(sd\right)$.

The variance can be used to determine the relation between the individual numbers with each other within a data set. In this, Javier's sample has more variability than Ercilia's sample.

(c) Explanation : 

Javier and Ercilia are supervisors at a shopping mall. Each of them was given the task of estimating the mean distance that shoppers live from the mall. They randomly surveyed

$100$shoppers. The samples yield are,

The histogram (a) has less variability and (b) has more variability.

Hence, the histogram (b) is Ercilia's samples.

(d) Explanation : 

Javier and Ercilia are supervisors at a shopping mall. Each of them was given the task of estimating the mean distance that shoppers live from the mall. They randomly surveyed $100$shoppers. The samples yield are,

The boxplot explains the range and the IQR, both are measures of the variations.

The IQR of the boxplot (a) =$14-1=13$

The IQR of the boxplot (b) = $9-4=5$

Hence, the boxplot (b) has more variability than (a).

Boxplot (b) shows Ercilia's samples.