Chapter 3 - Summarising Numerical Data
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- 1.The following is a set of measurements: 11.0, 11.4, 12.3, 10.5, 11.6, 11.2, 11.8, 11.1, 11.2, 11.3, 11.5 The mean value is closest to:
- A.
11.11
- B.
11.15
- C.
11.35
- D.
11.50
- E.
11.56
- F.
I don't know
- 2.The lifetime of Last Forever car batteries is approximately normally distributed with a mean of 24 months and a standard deviation of three months. If 2000 batteries are sold, the number expected to last less than 15 months is closest to:
- A.
3
- B.
8
- C.
15
- D.
30
- E.
80
- F.
I don't know
- 3.The lifetime of Last Forever car batteries is approximately normally distributed with a mean of 24 months and a standard deviation of three months. The percentage of batteries that can be expected to last less than 30 months is:
- A.
2.5%
- B.
16%
- C.
32%
- D.
95%
- E.
97.5%
- F.
I don't know
- 4.The lifetime of Last Forever car batteries is approximately normally distributed with a mean of 24 months and a standard deviation of three months. The percentage of batteries that can be expected to last less than 21 months is:
- A.
16%
- B.
32%
- C.
50%
- D.
68%
- E.
95%
- F.
I don't know
- 5.The lifetime of Last Forever car batteries is approximately normally distributed with a mean of 24 months and a standard deviation of three months. The percentage of batteries that can be expected to last between 18 and 30 months is:
- A.
16%
- B.
32%
- C.
50%
- D.
68%
- E.
95%
- F.
I don't know
- 6.The lifetime of Last Forever car batteries is approximately normally distributed with a mean of 24 months and a standard deviation of three months. The percentage of batteries that can be expected to last more than 24 months is:
- A.
16%
- B.
32%
- C.
50%
- D.
68%
- E.
95%
- F.
I don't know
- 7.In a normal distribution, approximately 16% of values lie:
- A.
Within one Standard Deviation of the mean
- B.
Within two Standard Deviations of the mean
- C.
Within two Standard Deviations of the mean
- D.
More than one Standard Deviation above the mean
- E.
More than two Standard Deviations below the mean
- F.
I don't know
- 8.In a normal distribution, approximately 95% of values lie:
- A.
Within one Standard Deviation of the mean
- B.
Within two Standard Deviations of the mean
- C.
Within three Standard Deviations of the mean
- D.
More than one Standard Deviation above the mean
- E.
More than two Standard Deviations below the mean
- F.
I don't know
- 9.A student’s standardised score on a test was –2. The mean score on the test was 20 marks with a standard deviation of 3. Her actual mark on the test was:
- A.
11
- B.
14
- C.
17
- D.
18
- E.
26
- F.
I don't know
- 10.A student’s mark on a test is 60. The mean mark for their class is 75 and the standard deviation is 6. Their standard score is:-
- A.
-15
- B.
-6
- C.
-2.5
- D.
2.5
- E.
15
- F.
I don't know
- 11.It would not be appropriate to determine the mean and standard deviation of a group of women’s:
- A.
Heights
- B.
Age at leaving school
- C.
Weights
- D.
Place of residence
- E.
Time spent on leisure activities
- F.
I don't know
- 12.
The histogram above shows the distribution of the amount spent on gambling by a large sample of gamblers. For this distribution, the mean would be:- A.
Less than the median
- B.
Approximately equal to the median
- C.
Greater than the median
- D.
Less than $1000
- E.
Less than $10 000
- F.
I don't know
- 13.For this set of test marks: 20, 21, 13, 15, 16, 24, 17 the actual value of the standard deviation, correct to one decimal place, is:
- A.
2.1
- B.
2.7
- C.
3.5
- D.
3.8
- E.
3.9
- F.
I don't know
- 14.For this set of test marks: 20, 21, 13, 15, 16, 24, 17 an estimate of the standard deviation (based on the range) is
- A.
2.5
- B.
2.75
- C.
3.0
- D.
5.5
- E.
11.0
- F.
I don't know
- 15.For this set of test marks: 20, 21, 13, 15, 16, 24, 17 the mean value is:
- A.
16
- B.
17
- C.
18
- D.
19
- E.
20
- F.
I don't know
- 16.The heights of a group of 256 junior athletes is approximately normally distributed with a mean of 157 cm and a standard deviation of 3 cm. The number of junior athletes with heights greater than 154 cm is around:
- A.
82
- B.
128
- C.
175
- D.
215
- E.
250
- F.
I don't know
- 17.The heights of a group of 256 junior athletes is approximately normally distributed with a mean of 157 cm and a standard deviation of 3 cm. The number of junior athletes with heights less than 151 cm is around:
- A.
3
- B.
6
- C.
12
- D.
128
- E.
250
- F.
I don't know
- 18.The heights of a group of 256 junior athletes is approximately normally distributed with a mean of 157 cm and a standard deviation of 3 cm. The percentage of the junior athletes with heights between 148 and 166 cm is:
- A.
0.03%
- B.
50%
- C.
68%
- D.
95%
- E.
99.7%
- F.
I don't know
- 19.In a normal distribution, approximately 32% of values lie:
- A.
Within one Standard Deviation of the mean
- B.
Within two Standard Deviations of the mean
- C.
Within three Standard Deviations of the mean
- D.
More than one Standard Deviation above or below the mean
- E.
More than two Standard Deviations above or below the mean
- F.
I don't know
- 20.In a normal distribution, approximately 2.5% of values lie:
- A.
Within one Standard Deviation of the mean
- B.
Within two Standard Deviations of the mean
- C.
Within three Standard Deviations of the mean
- D.
More than one Standard Deviation above the mean
- E.
More than two Standard Deviations above the mean
- F.
I don't know
- 21.In a normal distribution, approximately 0.3% of values lie:
- A.
Within one Standard Deviation of the mean
- B.
Within two Standard Deviations of the mean
- C.
Within three Standard Deviations of the mean
- D.
More than three Standard Deviations above or below the mean
- E.
More than two Standard Deviations above or below the mean
- F.
I don't know
- 22.In a normal distribution, approximately 95% of values lie:
- A.
Within one Standard Deviation of the mean
- B.
Within two Standard Deviations of the mean
- C.
Within three Standard Deviations of the mean
- D.
More than one Standard Deviation above the mean
- E.
More than two Standard Deviations below the mean
- F.
I don't know
- 23.A student’s standardised score on a test is –0.5. The mean mark for their class is 68 and the standard deviation is 4. Their test score is:
- A.
60
- B.
64
- C.
66
- D.
67.5
- E.
70
- F.
I don't know
- 24.A student’s mark on a test is 75. The mean mark for their class is 68 and the standard deviation is 4. Their standardised score is:
- A.
–2.5
- B.
–1.75
- C.
0
- D.
1.75
- E.
2.5
- F.
I don't know
- 25.It is reasonable to use the mean measure of the centre of a distribution:
- A.
When the distribution is negatively skewed
- B.
When the distribution is positively skewed
- C.
When the distribution is symmetric
- D.
When the distribution is symmetric with outliers
- E.
Always
- F.
I don't know
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