Answer:
The standard deviation for the distribution of girths is
about the same for both male and female pigs.
Step-by-step explanation:
Step 1
We will interprete the dotplots
For the Male pigs
24, 26, 26, 26, 26, 26, 26, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 32
Range
Maximum value - Minimum value
= 32 - 24
= 8
IQR = Interquartile range = Q3 - Q1
Q1 formula = 1/4(n + 1)th
=n = 25
= 1/4(25 + 1)
= 1/4(26)
= 26/4
= 6.5
This mean the value is between the 6th and 7th value
6th value = 26
7th value = 26
Q1 = 26 + 26/2
Q1 = 26
Q3
Q3 formula = 3/4(n + 1)th
=n = 25
= 3/4(25 + 1)
= 3/4(26)
= 78/4
= 19.5
This mean the value is between the 19th and 20th value
19th value = 30
20th value = 30
Q3= 30+ 30/2
= 30
IQR = 30 - 26
= 4
Standard deviation
Mean
First we find the mean
= 24+ 26+26+ 26+ 26+ 26+26+28+ 28+ 28+ 28+28+ 28+ 28+28+ 28+28+28+30+ 30+30+ 30+30+30+32/28
= 700/25
= 28
Standard deviation Formula = √(x - mean)²/n - 1
= √[(24-28)² + (26- 28)² + (26 -28)² + (26 - 28)² +................ (32 - 28)²]/25 - 1
= √(16 + 4 + 4+ 4+ 4+4+ 4+0+ 0+ 0+ 0+0+ 0+ 0+ 0+0+0+0+ 4+ 4+4+4+4+ 4+ 16)/25 - 1
= √80/25 - 1
=√3.333333333
1.825741858
Female Pigs
21, 23, 23, 23,23,23,23,25, 25, 25, 25, 25, 25, 25, 25, 25, 25,25, 27, 27, 27, 27,27, 27, 29
Range:
Maximum value - Minimum value
= 29 - 21
8
IQR
IQR = Interquartile range = Q3 - Q1
Q1 formula = 1/4(n + 1)th
=n = 25
= 1/4(25 + 1)
= 1/4(26)
= 26/4
= 6.5
This mean the value is between the 6th and 7th value
6th value = 23
7th value = 23
Q1 = 23 + 23/2
Q1 = 23
Q3
Q3 formula = 3/4(n + 1)th
=n = 25
= 3/4(25 + 1)
= 3/4(26)
= 78/4
= 19.5
This mean the value is between the 19th and 20th value
19th value = 27
20th value = 27
Q3= 27+ 27/2
Q3 = 27
IQR = 27 - 23
= 4
First we find the Mean
=(21+23+23+23+23+23+23+25+ 25+ 25+ 25+25+ 25+ 25+ 25+25+25+25+27+27+ 27+27+27+ 27+29)/25
= 625/25
= 25
Standard deviation Formula = √(x - mean)²/n - 1
= √[(21-25)² + (23- 25)² + (23 -25)² + (23 - 25)² +................ (29 - 25)²]/25 - 1
= √(16 + 4 + 4+ 4+ 4+4+ 4+0+ 0+ 0+ 0+0+ 0+ 0+ 0+0+0+0+ 4+ 4+4+4+4+ 4+ 16)/25 - 1
= √80/25 - 1
=√3.333333333
1.825741858
Looking at the calculation above and comparing both the girths from the male and female
We can conclude that: The standard deviation for the distribution of girths is
about the same for both male and female pigs which is 1.825741858
