Question

Julian works as a commercial analyst for the giant American retailer Walmart. He conducts a study looking at the average mumber of minutes a sample of customers spend on the Walmart shopping app each week. To form the sample group. Julian segments customers into age brackets, and then uses random number generator software to select 15 customers from each bracket.(a) State the sampling method Julian uses in his study. Julian presents the results of his study in a box-and-whisker diagram, as shown.10 20 30 40 50 6080 90 100 110 120time spent on the app per week (minutes)(b) Write down the median time spent on the app per week. (c) Find the interquartile range. The customer in the sample with the highest average weekly usage uses the app for an average of 120 minutes each week.(d) Determine if this customer is considered an outlier in the sample.

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define the samoling method Julian uses in his study.

In Random sampling individual is chosen entirely by chance and each member of the population has an equal chance, or probability, of being selected. One way of obtaining a random sample is to give each individual in a population a number, and then use a table of random numbers to decide which individuals to include.

Since Julian uses a random number generator, hence, the sampling method is used is Random Sampling Method.

(a) Random Sampling Method

STEP 2: Find the median

The median of a boxplot is given as shown below:

The median is given as the point in the middle of the box with a straight vertical line, hence the median of the given box plot is 60.

Median = 60

STEP 3: Find the interquartile Range

The Interquartile range is given as the difference between Q1 and Q3, this is calculated as:

`\begin{gathered} Q1=40 \\ Q3=70 \\ IQR=70-40=30 \end{gathered}`

Hence, the interquartile Range is given as 30.

Interquartile Range = 30

STEP 4: Determine if the customer with app usage of 120 minutes is an outlier

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. The number within the box plot are not regarded as outlier. Since 120 is within the box plot, therefore it is not an outlier.

Therefore, the customer is not considered as an outlier.