MATHEMATICS EXERCISE


MATHEMATICS EXECISE

Attempt all the questions.

  1. A sample consist the following numbers, 2,4,7,3,5,6,3,6,10,7,8,9,3,4,3. Find

    1. the mode, median and mean,

    1. Standard deviation of the sample.

  1. Two independent events are such that the probability of both occurring is 1/6 and the probability of neither occurring is 1/3. Find the probability of each occurring.

  1. (a) Use the trapezium rule with five sub-intervals to estimate, correct to three decimal places.
(b)        (i) Find the value of , to three decimal places.

(ii) Calculate the percentage error in your estimation in (a) above.

(iii) Suggest two ways of reducing the percentage error.

  1. The table below shows delivery charges by a courier company.

Mass (gm)
200
400
600
Charges (shs)
700
1200
3000

Using linear interpolation or extrapolation, find the:

(a)    Delivery charge of a parcel weighing 352 gm.

(b)   Mass of a parcel whose delivery charge is shs 3,300.

5.      X and Y are judges at a beauty contest in which there were 10 competitors. Their rankings are shown below.
Competitor
A
B
C
D
E
F
G
H
I
J
X
4
9
2
5
3
10
5
7
8
1
Y
6
10
5
8
1
9
7
4
5
3

(a)    Plot a scatter diagram for the data. Comment on the relationship
between the rankings of the two judges.
       Draw a line of best fit through the points of the scatter diagram.

(b) Calculate a coefficient of rank correlation between these two sets of
ranks and comment briefly on your result.

6.      In the table is an extract of part of ln x to base e, lnex.

X
50.00
50.20
50.50
50.80
Ln ex
3.9120
3.9160
3.9220
3.9279

     Use linear interpolation or extrapolation to estimate:

(i)                 lne50.759.

(ii)               the number whose natural logarithm is 3.9119.

  1. The heights (in cm) of people in a certain sub-county were recorded as in the frequency table below:

Heights (cm)
Frequency (f)
149 – 152
5
153 – 156
17
157 – 160
20
161 – 164
25
165 – 168
15
169 – 172
6
173 – 176
2

a.       Estimate the mean height and standard deviation of the candidates.

b.      Plot a cumulative frequency curve (Ogive).

c.       Use your Ogive in (b) above to estimate the:
(i)                 median,

(ii)               range of the height of the middle 50% of the candidates.

  1. The table below shows consumer commodities bought by the Headmaster of Tip Top High school.

Commodity
Weight
Price
1990
Price
1992 = 100
A
30
1000
1100
B
5
100
80
C
10
30
20

(ii)         Calculate the weighted average price relative index.

(iii)       If the Headmaster bought a fourth commodity in 1992 worth Sh.2000, what is likely to have been its cost in 1990?

Subscribe to: Posts (Atom)