A survey of 20 randomly selected full-time Joliet Junior

A survey of 20 randomly selected full-time Joliet Junior College students was conducted in the Fall
2000 semester asking the weekly spending ($) on entertainment. The results were as follows:
21, 54, 64, 33, 65, 22, 39, 67, 54, 22, 28, 28, 75, 50, 27, 21, 26, 13, 38, 11.
(a) (1 mark) Build a stem and leaf plot in the space provided. Use the first digit for the stem:
2 1 1 2 2 6 7 8 8
3 3 8 9
4
5 0 4 4
6 4 5 7
7 5
(b) (1+1) The mode is _21, 54, 22, 28_while the median is _30.5_
(c) (1 mark) Calculate the sample mean
x
:

758 = 37.9
20

(d) (2 marks) Calculate the sample standard deviation, s, using the formula

1
( )
( )
2
2
−
?
? −
n
n
x
x
i
i

:

(e) (2 marks) Re-calculate the sample standard deviation, s, with the “reasoning formula”
1
( )
2
−
? −
n
x x i
: (show

your work)

2. (i) (1 + 2 marks) The following data represent the red blood cell count (M/μL) for 20 randomly
selected dogs
6.2, 6.0, 8.1, 6.8, 6.8, 6.8, 5.2, 5.6, 8.2, 7.0, 6.1, 6.1, 7.1, 6.6, 6.1, 6.9, 4.2, 5.3, 6.3, 7.5
Construct a frequency distribution that has 5 classes.
The range is ____________________ The class width will be _________________________
CLASS LIMITS Midpoint (xm) Frequency (f)

4.2 – 1 5.00
5.2 1 5.00
6.1 3 15.00
6.8 3 15.00
8.2 1 5.00

(ii) (1 mark) The approximation for the sample mean
g
x
, is:

(a) 6.15 (b) 6.47 (c) 6.75 (d) 6.32
(iii) (1 mark) The approximation for the sample standard deviation
g
s
, is:
(a) 0.685 (b) 0.95 (c) 0.768 (d) 0.88

(iv) (1 mark) The grouped mode is
(a) 7 (b) 6.95 (c) 6.15 (d) 6
(v) (1 mark) The boundaries of the second class are .......................................................
3. The normal monthly precipitation (in inches) for all the 10 cities in a region is listed below
4.8, 2.6, 1.5, 1.8, 1.8, 3.3, 5.1, 1.1, 1.8, 2.5
(i) [1] the data represent a (sample, population) ______________________________
(ii) (1 mark) The mean monthly precipitation is

(iii)(1 mark) The standard deviation is

(iv) (1 mark) Find the coefficient of variation
4. (1 mark) If a researcher wishing to draw a sample from sequentially numbered invoices uses a random
starting point, then draws every 50th invoice, he has thus drawn a _____ sample.
A. simple random B. cluster C. stratified D. systematic E. none of the above
5. (1 mark) The amount of time needed to run the Toronto marathon is an example of which type of variable?
(a) discrete (b) qualitative (c) continuous (d) none of the above

6. (1 mark) The scores that have the greatest effect on the value of the variance are those
a) above the mean b) below the mean c) nearest the mean d) farthest from the mean

7. The number of cars that arrived at a McDonald’s drive through between 11:50 A.M. and 12:00 noon on 30
randomly selected weekdays are as follows:
1, 3, 2, 8, 6, 6, 6, 3, 3, 1, 5, 6, 3, 3, 1, 4, 8, 5, 3, 5, 2, 6, 7, 5, 8, 7, 8, 3, 2, 3.
(i) [1] Summarize the data using frequencies and relative frequencies (round to 3 decimals if needed).

Number of cars Frequency Relative frequency
1
2
3
4
5
6
7
8

ii) (1 mark) On how many weekdays were there at least 5 cars arriving at the drive through?
(a) 11 (b) 15 (c) 16 (d) 19
iii) (1 mark) What percentage of weekdays showed 4, 5, or 6 cars arriving at the drive through?
(a) 0.3 (b) 30% (c) 0.333 (d) 33.3%
iv) (1 mark) What percentage of weekdays showed less than 3 cars arriving at the drive through?