Maths Statistics Paper

Question1: Frequency Distribution. Histograms, Cumulative Frequency and Ogives.

1)

a) 799
b) 1000
c) 900+9992 = 949.5
d) Lower Class Boundary=1100-0.5 =1099.5 Upper Class Boundary=1199.5+0.5=1199.5
e) 100
f) 76
g) 62400×100=15.5
h) 600-699, the fourth class has the largest frequency of 76.
i)14+46+58400 ×100=29.5%
j) 48+22+6400 ×100=19.0%
k) 4002=200 200 lie in the fifth class interval 700-799 ∴The median lies in this interval.
=l+n2-cff×h
=700+200-19468×99
=708.735
l) L.Limit | U.Limit | Frequency | midpoint | fx | 300 | 399 | 14 | 349.5 | 4893 | 400 | 499 | 46 | 449.5 | 20677 | 500 | 599 | 58 | 549.5 | 31871 | 600 | 699 | 76 | 649.5 | 49362 | 700 | 799 | 68 | 749.5 | 50966 | 800 | 899 | 62 | 849.5 | 52669 | 900 | 999 | 48 | 949.5 | 45576 | 1000 | 1099 | 22 | 1049.5 | 23089 | 1100 | 1199 | 6 | 1149.5 | 6897 | | | ∑f 400 | | ∑fx 286000 |
Mean=∑fx ∑f =286000400=715
m)
Lifetime | Frequency | C. Frequency | 300-399 | 14 | 14 | 400-499 | 46 | 60 | 500-599 | 58 | 118 | 600-699 | 76 | 194 | 700-799 | 68 | 262 | 800-899 | 62 | 324 | 900-999 | 48 | 372 | 1000-1099 | 22 | 394 | 1100-1199 | 6 | 400 |

n) Lifetime | Frequency | C. Frequency | % C. Frequency | 300-399 | 14 | 14 | (14 ÷ 400) x 100= 3.5 % | 400-499 | 46 | 60 | (60 ÷ 400) x 100= 15 % | 500-599 | 58 | 118 | (118 ÷ 400) x 100= 29.5 % | 600-699 | 76 | 194 | (194 ÷ 400) x 100= 48.5 % | 700-799 | 68 | 262 | (262 ÷ 400) x 100= 65.5 % | 800-899 | 62 | 324 | (324 ÷ 400) x 100= 81 % | 900-999 | 48 | 372 | (372 ÷ 400) x 100= 93 % | 1000-1099 | 22 | 394 | (394 ÷ 400) x 100= 98.5 % | 1100-1199 | 6 | 400 | (400 ÷ 400) x 100= 100 % |

o)

p)

2a&b)

Class | Frequency | 0.725-0.729 | 9 | 0.730-0.734 | 17 | 0.735-0.739 | 23 | 0.740-0.744 | 8 | 0.745-0.749 | 3 |

2c)

Question 2 Measures of Central Tendency

P55 is located at the 33rd ordered Term = 61

D8 is the equal to P80,