Download MDM4U1 Central Tendency Test 1

MDM4U1: Central Tendency Practice Test
1. A family has eight children. The ages are 9, 11, 8, 15, 14, 12, 17, 14.
Find the measures of central tendency for the data. Find the range of the
data.
2. Find mean and standard deviation of the following data:
Class interval
Frequency
1–5
2
6 – 10
5
11 – 15
2
16 – 20
1
3. The angiogram is a standard diagnostic test used in clinical medicine
to detect stroke in patients. This test has some risks for the patient, and
several noninvasive techniques have been developed that are hoped to be
as effective as the angiogram. One such method utilizes that
measurement of cerebral blood flow (CBF) in the brain, since stroke
patients tend to have lower levels of CBF than normal. Among healthy
people, CBF is normally distributed with mean 75 and standard
deviation 17. Patients are classified as being at risk for stroke if their
CBF is below 40. What proportion of normal patients will be mistakenly
classified as being at risk for stroke?
4. Maple tree diameters in a forest area are normally distributed with
mean 10 inches and standard deviation 2.2 inches. Find the percent of
trees having a diameter greater than 15 inches.
5. Name the measurements of central tendency for the distributions
below. Justify your choices:
6. The mean age of 120 teachers in a school is 38 years with a standard
deviation of 5.3. Six of the teachers in the school are over 54 years of
age. Is the distribution of the teachers’ ages normal? Explain.
7. The masses of Burgerville’s half-pounders are normally distributed.
Of these burgers, 33% have masses greater than 253.52 g and 40.9% of
them have masses less than 248.16 g. Find the mean and standard
deviation of the half-pounder masses.
8. A history test was taken by 51 students. The scores ranged from 50 to
95 and were classified into 5 classes of width 6 units. The resulting
frequency distribution appears below. Find variance and standard
deviation for the sample.
Class
Class mark, xi
Frequency, fi
1
55
5
2
66
13
3
78
22
4
87
10
5
93
1
Total
9. Glaucoma is a disease of the eye that is manifested by high intraocular
pressure. The distribution of intraocular pressure in the general
population is approximately normal with mean 16 mm Hg and standard
deviation 3.2 mm Hg. If the normal range for intraocular pressure is
between 10 and 22 mm Hg, than what percentage of the general
population would fall within this range?
10. What can be said about a sample of observations whose standard
deviation is zero?
11. Compare the following measures of dispersion: standard deviation,
variance, and range. What are the benefits and disadvantages of each
measure?
12. Approximately what percentage of the data on a normal distribution
fall
a) below the mean?________________________________
b) within + 1 standard deviation from the mean? _________________
13. Are the following statements true or false? Justify your choices. You
may wish to support your answers with diagrams.
a) A negative z score always yields a negative percentile. ________
b) A positive z score always yields a percentile rank above 50. ________
c) A negative z score always indicates that the raw score is below the
mean. ______
d) Between z scores of + 3.00 under the normal curve can be found
almost the entire distribution. _____________
Answers:
1. Mean = 12.5, median = 13, mode = 14, range = 9
2. Mean = 9; standard deviation = 4.6
3. 2%
4. 1.15%
5. Mode, median, mean;
mean, median, mode
6. Not normal distribution, it should be 0.15% of the teachers over 54
years old.
7. 8
8. Variance = 98.2, standard deviation = 9.91
9. 93.9%