Chapter 1.2, Problem 48E

(a)

To determine

To make: a stemplot using tens of dollars

Answer to Problem 48E

Stem	Leaf
0	3	9	9
1	1	3	4	5	6	7	7	8	8	9
2	0	0	0	1	2	3	4	5	5	6	6	8	8	8	8
3	2	5	6	9	9
4	1	3	4	5	5	7	9
5	0	3	5	9
6	1
7	0
8	3	6	6
9	3

Explanation of Solution

Given:

3.11	8.88	9.26	10.81	12.69	13.78	1523	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	58.64	39.16	41.02	42.97	44.08	44.67	45.40	46.69	48.65
50.39	5175	54.80	59.07	61.22	70.32	8170	85.76	86.37	93.34

Calculation:

To make a stemplot of these amounts, round each amount to the nearest dollar, so that tens of dollars as the stems and dollars as the leaves.

The stem-plot for dollars spent by 50 consecutive shoppers in super market is below:

Stem	Leaf
0	3	9	9
1	1	3	4	5	6	7	7	8	8	9
2	0	0	0	1	2	3	4	5	5	6	6	8	8	8	8
3	2	5	6	9	9
4	1	3	4	5	5	7	9
5	0	3	5	9
6	1
7	0
8	3	6	6
9	3

Conclusion:

Therefore, stem-plot is drawn.

(b)

To determine

To make: stemplot by splitting stems and which one shows the better shape

Answer to Problem 48E

Stem	Leaf
0	3
0	9	9
1	1	3	4
1	5	6	7	7	8	8	9
2	0	0	0	1	2	3	4
2	5	5	6	6	8	8	8	8
3	2
3	5	6	9	9
4	1	3	4
4	5	5	7	9
5	0	3
5	5	9
6	1
6
7	0
7
8	3
8	6	6
9	3

The distribution by splitting stem has become clearer.

Explanation of Solution

Calculation:

The stem-plot of the data by splitting stems is below:

Stem	Leaf
0	3
0	9	9
1	1	3	4
1	5	6	7	7	8	8	9
2	0	0	0	1	2	3	4
2	5	5	6	6	8	8	8	8
3	2
3	5	6	9	9
4	1	3	4
4	5	5	7	9
5	0	3
5	5	9
6	1
6
7	0
7
8	3
8	6	6
9	3

The distribution by splitting stem has become clearer. The distribution is asymmetric and irregular. The distribution is multimodal as it has more than two peaks. The split plot shows the shape of the distribution in a better way.

Conclusion:

Therefore, the distribution by splitting stem has become clearer.

(c)

To determine

To write: a few sentences about the amount of money spent by shoppers

Answer to Problem 48E

The shape describes the pattern in which amount of money is spent is very irregular.

Explanation of Solution

Calculation:

The shape describes the pattern in which amount of money is spent is very irregular. The range of expenditure varies from 3 dollars to 93 dollars $\left(93-3=90\right)$ . The spread is very high.