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1. Our first homework’s datas are shown below :
According to these datas, we will compute mode, average, median and sample variance.
Mode: The value that has the highest frequency.
# of 100 : 8
# of 140 : 1
# of 150 : 6
# of 170 : 2
# of 180 : 1
# of 200 : 10
# of 250 : 8
# of 270 : 1
# of 300 : 12 → mode is “ 300 ”
# of 350 : 5
# of 400 : 7
# of 450 : 1
# of 500 : 4
# of 550 : 1
Average : Dividing total number of our all datas to total data number that we collected.
(100∗8)+(140∗1)+(150∗6)+(170∗2)+(180∗1)+(200∗10)+(250∗8)+(270∗1)
+(300∗12)+(350∗5)+(400∗7)+(450∗1)+(500∗4)+(550∗1)+(600∗3)
70
=279,7142…≅280

2. Median: The middle value when we list our datas from smallest to largest.
푥̃ = x(n+1)/2 if n is odd
푥̃ =
푥
(푛
2
)
+ 푥
(푛
2
)+1
2
if n is even (n = total number of our datas)
Then 푥̃ is:
푥35 + 푥36
푥̃=
2
=
250+250
2
= 250
Sample variance: Measure of dispersion.
S2 =
Σ (푥푖−푥̅) 푛푖=1
푛−1
(n = total number of our datas)
Then S2 is :
S2 =
[(100−280)2 ∗8]+[(140−280)2 ∗1]+[(150−280)2 ∗6]+[(170−280)2 ∗2]+[(180−280)2 ∗1]
+[(200−280)2 ∗10]+[(250−280)2 ∗8]+[(270−280)2 ∗1]+[(300−280)2 ∗12]+[(350−280)2 ∗5]
+[(400−280)2 ∗7]+[(450−280)2 ∗1]+[(500−280)2 ∗4]+[(550−280)2 ∗1]+[(600−280)2 ∗3]
69