Preschool The ages (in months) at which 50 children were first enrolled in a preschool are listed below.
38 40 30 35 39 40 48 36 31 36
47 35 34 43 41 36 41 43 48 40
32 34 41 30 46 35 40 30 46 37
55 39 33 32 32 45 42 41 36 50
42 50 37 39 33 45 38 46 36 31
a. Construct a stem and leaf display for the data.
b. Construct a relative frequency histogram for these data. Start the lower boundary of the first class at 30 and use a class width of 5 months.
c. Compare the graphs in parts a and b. Are there any significant differences that would cause you to choose one as the better method for displaying the data?
d. What proportion of the children were 35 months (2 years. 11 months) or older, but less than 45 months (3 years. 9 months) of age when first enrolled in preschool?
e. If one child were selected at random from this group of children, what is the probability that the child was less than 50 months old (4 years. 2 months) when first enrolled in preschool?
(a)
To construct a stem and leaf display for the data given in the question.
Answer to Problem 1.28E
The stem and leaf display is below as:-
Stem | Leaf |
3 | 0 0 0 1 1 2 2 2 3 3 4 4 5 5 5 6 6 6 6 6 7 7 8 8 9 9 9 |
4 | 0 0 0 0 1 1 1 1 2 2 3 3 5 5 6 6 6 7 8 |
5 | 0 0 5 |
6 | |
7 | 8 |
Explanation of Solution
The set of data is given in the question.
Each observation in the data is dividedbetween the ones and the tens place. The number to the left is the stem and the number to the right is the leaf.
(b)
To construct a relative frequency histogram for the data given in the question.
Answer to Problem 1.28E
The relative frequency histogram is as follows:-
Explanation of Solution
The observations are given in the question.
By considering the observations, Relative frequency distribution is constructed with the lower boundary of the first class at 30 and the class width of 5 months.
(c)
To compare the graphs in (a) and (b) and also to find if there is any significant differences that would cause us to choose one as the better method for displaying the data.
Answer to Problem 1.28E
The graphs in (a) and (b) are both skewed to the right but in (a) the data is displayed in horizontal view and in (b) the data is displayed in the vertical view.
Yes, there is significant difference in the view and also the vertical view is more convenient way to display and understand the data i.e. in (b) than in (a).
Explanation of Solution
The graph in (a) is stem and leaf in which each observation in the data is divided between the ones and the tens place. The number to the left is the stem and the number to the right is the leaf. This is displayed in horizontal view.
And the graph in (b) is arelative frequency histogramfor a quantitative data set is a bar graph in which the height of the bar shows “how often” (measured as a proportion or relative frequency) measurements fall in a particular class or subinterval. This is displayed in vertical view.
Both the graphs are skewed to the right by looking at the graph in both the parts.
And also the data can be better understandable and easy to view in vertical form. Thus, the graph in part (b) is better method for displaying the data.
(d)
To calculate the proportion of the children who are
Answer to Problem 1.28E
The proportion of the children who are
Explanation of Solution
By looking at the relative frequency data from the histogram, we get that:-
Data | cumulative | |||||||
lower | upper | midpoint | width | frequency | percent | frequency | percent | |
25 | < | 30 | 28 | 5 | 0 | 0.0 | 0 | 0.0 |
30 | < | 35 | 33 | 5 | 12 | 24.0 | 12 | 24.0 |
35 | < | 40 | 38 | 5 | 15 | 30.0 | 27 | 54.0 |
40 | < | 45 | 43 | 5 | 12 | 24.0 | 39 | 78.0 |
45 | < | 50 | 48 | 5 | 7 | 14.0 | 46 | 92.0 |
50 | < | 55 | 53 | 5 | 2 | 4.0 | 48 | 96.0 |
55 | < | 60 | 58 | 5 | 1 | 2.0 | 49 | 98.0 |
60 | < | 65 | 63 | 5 | 0 | 0.0 | 49 | 98.0 |
65 | < | 70 | 68 | 5 | 0 | 0.0 | 49 | 98.0 |
70 | < | 75 | 73 | 5 | 0 | 0.0 | 49 | 98.0 |
75 | < | 80 | 77 | 5 | 1 | 2.0 | 50 | 100.0 |
50 | 100.0 |
That there are
Thus, we have,
(e)
To calculate the probability that the child was less than
Answer to Problem 1.28E
Explanation of Solution
To find the probability that the child was less than
First calculate the number of children who are less than
The number of children who are less than
Secondly we have to calculate the total number of children in the group that are
Thus, the probability that the child was less than
Therefore,
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Chapter 1 Solutions
Introduction to Probability and Statistics
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL