Answers

1.  
   1.  
      1. 0.1
      2. 0
      3. 0
      Return to question 1a
   2.  
      1. 2
      2. 2
      3. 2
      Return to question 1b
   3.  
      1. 2.8
      2. 2.5
      3. 3.9
      Return to question 1c
   4.  
      1. 154.3
      2. 154.3
      3. 152.3
      Return to question 1d
2.  
   1.  
      1. 0
      2. 0
      3. 0
      4. The mean, median and mode are equal. This distribution is almost symmetrical.
      Return to question 2a
   2.  
      1. 6.6
      2. 6.7
      3. 6.7
      4. Distribution is skewed left, so the mean is less than the median. The mode and median are the same. In skewed distributions, the median is the better measure of central tendency.
      Return to question 2b
   3.  
      1. 1.85
      2. 1
      3. 1
      4. The median and mode are the same. The distribution is skewed right, so the mean is more than the median. In skewed distributions, the median is the better measure of central tendency. In b) and c), the mean has been influenced by a few low and high values.
      Return to question 2c
3.  
   1.  
      1. 48
      2. 40 to 49
      Return to question 3a
   2.  
      1. 23
      2. 20 to 24
      Return to question 3b
4.  
   1. 72,186.5 Return to question 4a
   2. 74,729 Return to question 4b
   3. The measures are quite close together, given the size of each observation. The median probably gives the best indication of the data's centre, as there is a large diversity of observation values. The median would not be affected by the very large or very small values. Return to question 4c
   4. A government could use these measures when planning for building schools, hospitals and road construction. The government could also use them to help predict revenue intake from taxation. Return to question 4d
5.  
   1.  
      

      Table 1.  Math test results, marked out of 10 points

      Score (x)	Tally	Frequency (f)
      0
      1		2
      2		3
      3		4
      4		4
      5		4
      6		2
      7		10
      8		3
      9		6
      10		2
      Total		40

      Return to question 5a
   2. mean = 5.9, median = 7, mode = 7 Return to question 5b
   3. The median is higher than the mean because most of the observations have high values. The mean is influenced by the lower scores. The mode is equal to the median. Return to question 5c
6.  
   1. 36.2 to 34 (Note: interval sizes are not the same. If they were, the 15 to 24 interval would be the modal-class interval.) Return to question 6b
   2. 25 to 34 Return to question 6c
   3. All three results lie within the same interval, but distribution is skewed (or slanted) to the right. Return to question 6d
   4. The younger age groups, 15 to 19 and 20 to 24, are filled with students who are still in school or graduates who have not yet been able to get a job. The age groups after 25 to 34 contain a smaller proportion of unemployed people because these people have joined the work force full time and are no longer attending school. Return to question 6e
   5. Social welfare organizations might use these figures to plan employment programs catering to younger people. Return to question 6f
7.  
   1.  
      

      Table 2.  Hours spent per week doing unpaid household work

      Hours	No. of men (x)	Endpoint	Cumulative frequency	Cumulative percentage
      0 to < 5	1	5	1	1
      5 to < 10	18	10	19	19
      10 to < 15	24	15	43	43
      15 to < 20	25	20	68	68
      20 to < 25	18	25	86	86
      25 to < 30	12	30	98	98
      30 to < 35	1	35	99	99
      35 to < 40	1	40	100	100

      Return to question 7a
   2.  
      
      Return to question 7b
   3. The approximate median value is 17 hours. This indicates that the middle of the distribution is 17 hours. Return to question 7c
   4. The modal-class interval is 15 to < 20 hours. Return to question 7d
   5. The mean value is 16.8 hours. This indicates that the average number of hours that a married man spends doing unpaid household work is 16.8 hours. Return to question 7e
   6. The mean and median are very similar, and all measures lie in the modal-class interval. The distribution is almost symmetrical. Return to question 7f
   7. A survey could be conducted and analysed in a similar fashion. Then, the results of both surveys could be compared. Return to question 7g
8.  
   1. The modal-class interval is $10,400 to $15,599. (Note: interval sizes are not the same.) Return to question 8a
   2.  
      

      Table 3. Annual income of people aged 15 years and more

      Income ($)	Persons	Endpoint	Cumulative frequency	Cumulative percentage
      		0	0	0.0
      0 to < 2,080	114,195	2,080	114,195	9.4
      2,080 to < 4,160	44,817	4,160	159,012	13.1
      4,160 to < 6,240	45,862	6,240	204,874	16.9
      6,240 to < 8,320	139,611	8,320	344,485	28.4
      8,320 to < 10,400	114,192	10,400	458,677	37.8
      10,400 to < 15,600	148,276	15,600	606,953	50.0
      15,600 to < 20,800	123,638	20,800	730,591	60.2
      20,800 to < 26,000	121,623	26,000	852,214	70.2
      26,000 to < 31,200	103,402	31,200	955,616	78.7
      31,200 to < 36,400	73,463	36,400	1,029,079	84.8
      36,400 to < 41,600	59,126	41,600	1,088,205	89.7
      41,600 to < 52,000	68,747	52,000	1,156,952	95.3
      52,000 to < 78,000	56,710	78,000	1,213,662	100.0

      Return to question 8b
   3.  
      
      Return to question 8c
   4. The median annual individual income is approximately $15,500. Return to question 8d
   5. The mean annual income is $19,986. Return to question 8e
   6. It is difficult to compare the mode with the mean and median because of the difference between the sizes of the intervals. The mean is higher than the median because it is affected by the higher incomes. This means that the distribution is skewed or slanted to the right. Return to question 8f
   7. The median gives the most accurate picture of the data's centre because it is not influenced by extreme values. Return to question 8g
   8. Some possible answers include the following:
      • social welfare organisations interested in the number of low-income earners;
      • businesses interested in the number of high-income earners; and
      • governments and other service providers interested in data, broken down by such characteristics as age, sex and geographic area, in order to locate services appropriately. Return to question 8h