Q 48. Shopping spree A marketing consu... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 1: Q 48. (page 44)

Shopping spree A marketing consultant observed 50 consecutive shoppers at a supermarket. One variable of interest was how much each shopper spent in the store. Here are the data (in dollars), arranged in
increasing order:
(a) Round each amount to the nearest dollar. Then make a stem $50$ plot using tens of dollars as the stems and dollars as the leaves.
(b) Make another stem plot of the data by splitting stems. Which of the plots shows the shape of the distribution better?
(c) Write a few sentences describing the amount of money spent by shoppers at this supermarket.

Short Answer

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Part (a)

Part (b) The dispersion of the split stem has grown more obvious.

Part (c) The pattern in which money is spent is quite irregular, as described by the shape.

Step by step solution

Part (a) Step 1: Given information

Observation of $50$ consecutive shoppers at a supermarket.

3.11	8.88	9.26	10.81	12.69	13.78	15.23	15.62	17.00	17.39
18.36	18.43	19.27	19.50	19.54	20.16	20.59	22.22	23.04	24.47
24.58	25.13	26.24	26.26	27.65	28.06	28.08	28.38	32.03	34.98
36.37	38.64	39.16	41.02	42.97	44.08	44.67	45.40	46.69	48.65
50.39	52.75	54.80	59.07	61.22	70.32	82.70	85.76	86.37	93.34

Part (a) Step 2: Concept

Shape: The peak of the dot plot is at This means that during that season, the team's most common number of goals scored in games (known as the mode) was The United States women's soccer team scored between one and five goals in the majority of its games. The distribution, however, has a large tail to the right.

Centre: can be described by selecting a value that divides the observations in half, with the bigger half taking greater values and the smaller half taking lower values.

The spread of distribution indicates the amount of variability in the data. Giving the smallest and greatest values is one approach to describe the variability.

Part (a) Step 3: Explanation

Round each sum to the closest dollar, using tens of dollars for the stems and dollars for the leaves to construct a stem plot.

The stem-plot for dollars being spent in the supermarket by $50$ consecutive shoppers is as follows:

As a result, a stem plot is created.

Part (b) Step 1: Explanation

The following is a stem-plot of the data created by splitting stems:

As a result of detaching the stem, the dispersion has improved. The distribution is lopsided and imbalanced. The distribution is multimodal since there are more than two peaks. The distribution's form is more clearly depicted in the split-plot.

As a result of separating the stem, the dispersion has become apparent.

Part (c) Step 1: Explanation

The shape that describes the pattern in which money is spent is an extremely irregular shape. The amount spent ranges from three dollars to ninety dollars $(93 - 3 = 90)$ The dispersion is really wide.