Question

Use the following data on median values of single detached houses of Canadian residents in 20 census metropolitan areas in British Columbia and Ontario in 2017 (source: Statistics Canada) to prepare a statistical report. The data are reported in units of a hundred thousand dollars rounded to the nearest ten thousand dollars (so, for example, 5.7 represents $570,000).

Data: 5.7, 5.2, 12.6, 6.4, 3.7, 2.1, 2.9, 2.4, 4.2, 4.3, 2.9, 3.6, 2.6, 4.2, 4.2, 2.7, 2.5, 2.2, 7.2, 1.9. ):

1. A dotplot or a histogram of the data. Note that you’ll have to group the data into suitable, equal-sized intervals before drawing your graph.

2. A pie graph of the data showing the percentages of the sample in the following categories: 1-3, 3-5, 5-7, 7-10, and 10 or higher.

3. The mean and the median, together with a brief discussion of which of these is the more appropriate measure of what is typical or representative for this dataset.

4. The 5-number summary of the data (i.e., the minimum, lower quartile, median, upper quartile, and maximum

5. The range of the data and the inter-quartile range of the data, together with a brief discussion of exactly what the inter-quartile range represents for this dataset.

6. The following probability calculations, including reasoning. Suppose we select one census metropolitan area at random from the sample of 20. What is the probability that it has a single detached house median value greater than $500k?

7. Suppose we select one census metropolitan area at random from the sample of 20. What is the probability that it has a single detached house median value greater than $500k or less than $200k? (2) Suppose we select two census metropolitan areas at random from the sample of 20. What is the probability that both have a single detached house median value greater than $500k?

Answer 1

1. A dotplot or a histogram of the data. Note that you’ll have to group the data into suitable, equal-sized intervals before drawing your graph.

Frequency Table
Class	Count
1-3.3	9
3.4-5.7	8
5.8-8.1	2
8.2-10.5	0
10.6-12.9	1

2. A pie graph of the data showing the percentages of the sample in the following categories: 1-3, 3-5, 5-7, 7-10, and 10 or higher.

1-3	9
3-5	6
5-7	3
7-10	1
10 or higher	1

3. The mean and the median, together with a brief discussion of which of these is the more appropriate measure of what is typical or representative for this dataset.

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

1.9   2.1   2.2   2.4   2.5   2.6   2.7   2.9   2.9   3.6   3.7   4.2   4.2   4.2   4.3   5.2   5.7   6.4   7.2   12.6   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Since our data is skewed(right-skewed )hence median would be better.

4. The 5-number summary of the data (i.e., the minimum, lower quartile, median, upper quartile, and maximum

Ordering the data from least to greatest, we get:

1.9   2.1   2.2   2.4   2.5   2.6   2.7   2.9   2.9   3.6   3.7   4.2   4.2   4.2   4.3   5.2   5.7   6.4   7.2   12.6   

1. the minimum is 1.9

2.the maximum is 12.6

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

1.9   2.1   2.2   2.4   2.5   2.6   2.7   2.9   2.9   3.6   3.7   4.2   4.2   4.2   4.3   5.2   5.7   6.4   7.2   12.6   

So, the bottom half is

1.9   2.1   2.2   2.4   2.5   2.6   2.7   2.9   2.9   3.6   

The median of these numbers is

3.First quartille=2.55

4.median=3.65

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

1.9   2.1   2.2   2.4   2.5   2.6   2.7   2.9   2.9   3.6   3.7   4.2   4.2   4.2   4.3   5.2   5.7   6.4   7.2   12.6   

So, the upper half is

3.7   4.2   4.2   4.2   4.3   5.2   5.7   6.4   7.2   12.6   

The median of these numbers is

5. Third quartile=4.75

Minimum First quartile Median(second quartile) Third quartile Maximum

1.9 2.55 3.65 4.75 12.6

5. The range of the data and the inter-quartile range of the data, together with a brief discussion of exactly what the inter-quartile range represents for this dataset.

The lowest value is 1.9

The highest value is 12.6

The range = 12.6 - 1.9 = 10.7

The interquartile range is the difference between the third and first quartiles.

The third quartile is 4.75

The first quartile is 2.55

The interquartile range = 4.75 - 2.55 = 2.2

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