Question

Shopping spree The figure displays computer output for data on the amount spent by 50 grocery shoppers.

(a) What would you guess is the shape of the distribution based only on the computer output? Explain.

(b) Interpret the value of the standard deviation.

(c) Are there any outliers? Justify your answer.

Short answer

Part (a) Right Skewed

Part (b) The average amount spent by 50 grocery buyers in the sample will differ by 21.70 dollars from the mean of 34.70 dollars.

Part (c) Yes.

Step-by-step solution

Part (a) Step 1. Given information.

The given information is:

Part (a) Step 2. Guess the shape of the distribution.

The values of mean and median for the given data are 34.70 and 27.86 respectively.

We can see that the mean value is higher than the median, from it we can conclude that the skewness of the distribution is towards the right.

Its reason is that the mean may be influenced by the unusual data values if we compare it with the median making the mean value larger than the median.

Part (b) Step 1. Interpret the value of the standard deviation.

The standard deviation is a measure of how much the data values deviate from the mean.

The amount spent by 50 grocery shoppers in the sample is expected to vary by 21.70 dollars on average, compared to the mean of 34.70 dollars.

Part (c) Step 1. Identify any outliers in the distribution.

$$\begin{gathered} Q_1=19.27,Q_3=45.40 \\ IQR=45.40-19.27 \\ =26.13 \end{gathered}$$

Observations that are more than 1.5 times the IQR above or below Q1 are considered outliers.

$$\begin{gathered} Q_3+1.5IQR=45.40+1.5\left(26.13\right) \\ =84.595 \\ {Q}_1-1.5IQR=19.27-1.5\left(26.13\right) \\ =-19.925 \end{gathered}$$

We know that the maximum value is 93.34 which is larger than 84.595 making 93.34 an outlier.

Therefore, we can say that outliers are present in this given data.