Question
Asked Sep 5, 2019

Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on the next page are based on random samples of size 30,50 and 100 from the same population.

a. Using the midpoint labels of the three histograms, what would you say about the estimated range of population data from smallest to largest? Does the bulk of the data seem to be between 8 and 12 all in three histograms? 

b. The population distribution from which the samples were drawn is symmetric and mound shaped, with the top of the mound at 10,95% of the data between 8 and 12, and 99.7% of data between 7 and 13. How well does each histogram reflect these characteristics?

(ii) Sample of size 50
(i) Sample of size 30
12
7
8 -
6
6
4
T3
2
2
mott
1
11
10
12
0
9
7
0
12
11
10
9
(iii) Sample of size 100
20
15
10
5+
12
11
10
9
8O
10
Frequency
LO
Frequency
4
25
Frequency
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(ii) Sample of size 50 (i) Sample of size 30 12 7 8 - 6 6 4 T3 2 2 mott 1 11 10 12 0 9 7 0 12 11 10 9 (iii) Sample of size 100 20 15 10 5+ 12 11 10 9 8O 10 Frequency LO Frequency 4 25 Frequency

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Expert Answer

Step 1

a.

Range:

The range is the difference between the largest and smallest values of the data distribution.

Step 2

Using the midpoint labels of the three histograms, the range of the popu...

Smallest Largest
Histogram (i)
Histogram (ii)
Histogram (iii)
8
12
7
12
7
13
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Smallest Largest Histogram (i) Histogram (ii) Histogram (iii) 8 12 7 12 7 13

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