EPPD2023
EXERCISES LECTURE 3
Numerical Descriptive Statistics
INSTRUCTION: Answer All questions.
1. The number of sick days due to colds and flu last year were recorder by a sample for 15 adults. The data are:
5 7 0 3 15 6 5 9
3 8 10 5 2 0 12
Compute the mean, median and mode.
2. Given the data for the population as below:
7, 5, 11, 8, 3, 6, 2, 1, 9, 8
a. Compute the mean.
b. Compute the standard deviation.
3. A random sample of 12 joggers was asked to keep track and report the number of miles they ran last week. The responses are
5.5 7.2 1.6 22.0 8.7 2.8
5.3 3.4 12.5 18.6 8.3 6.6
a. Compute the three statistics that measure central location.
b. Briefly describes what each statistics tells you.
c. What is the shape for data distribution?
4. The table below shows the income received by the instructors at 8 Swimming Training Centre.
|
Income (RM)
|
7600
|
3900
|
5300
|
4000
|
7200
|
2300
|
5100
|
|
Number of instructors
|
50
|
30
|
40
|
25
|
60
|
15
|
35
|
Calculate weighted mean for the income.
5. Assume there are two sets of sample, A and B as shown in the table below.
|
A
|
27
|
27
|
25
|
12
|
15
|
10
|
20
|
37
|
31
|
35
|
|
B
|
1
|
3
|
2
|
16
|
18
|
16
|
16
|
4
|
16
|
18
|
a. Calculate range, variance, standard deviation for both samples.
b. Using coefficient of variation, explain which sample has higher dispersion of data
c. Determine the shape of data distribution for both samples.
6. The manufacturer of an extended-life lightbulb claims the bulb has an average life of 12,000 hours and 500 hours. If the distribution is bell shaped and symmetrical, what is the approximate percentage of these bulbs that will last
a. between 11,000 and 13,000 hours?
b. over 12,500 hours?
c. less than 11,000 hours.?
d. between 11,500 and 13,000 hours?
7. The average price of a new car is RM36,000 with a standard deviation of RM4,100. What percentage of the price of the car sold is between RM22,000 and RM50,000. Assume the car price distribution is sloping to the right.
8. Assume that the mean weight of a 1-year-old infant is normally distributed with mean and standard deviation of weight, equal to 9.5 kg and 1.1 kg, respectively. Calculate the percentage of babies who weigh:
i) Less than 8.4kg.
ii) Between 7.3 and 11.7kg.
iii) Exceed12.8kg.
9. The following is the total profit earned by 2 individuals for a period of 4 months.
|
Months
|
Profit (RM)
|
|
1
|
2
|
3
|
4
|
|
A
B
|
260
400
|
240
100
|
250
500
|
250
200
|
a) Calculate the coefficient of variation for profit.
b) Whose profit is stable?
10. Suppose you bought a stock 6 years ago at RM12 per unit. Table below shows the stock price at the end for each year.
|
Year
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Price
|
10
|
14
|
15
|
22
|
30
|
25
|
a. Calculate the rate of return for each year
b. Calculate the arithmetic mean for the rate of return.
c. Compute the geometric mean of the rates of return.