Answer:
i) mean = 2.466667 = 3 (approx.)
ii) median = 2
iii) standard deviation = 1.241468
iv) 1st quartile (Q1) = 2
v) 3rd quartile (Q3) = 3
vi) Percentage of respondent having <3 siblings = (35/60)*100 = 58.3%
vii) 20% of all respondents have had at most how many siblings = 1 sibling
Step-by-step explanation:
The first step is to form a frequency distribution from the information given. This is as follows:
Number of siblings | Frequency
1 | 13
2 | 22
3 | 15
4 | 6
5 | 3
6 | 0
7 | 1
Having done this, we can compute the mean, median and standard deviation.
i) Mean ([tex]\bar{x}[/tex]) = [tex]\frac{\sum{fx}}{\sum{f}}[/tex],
Where f - frequency and x - is the number of siblings. Thus, fx is a f multiply by x.
ii) We do the same for median = L + {n/2 - Cf}c
That is, L - is the lower class boundary of the median class, n is the sample size, Cf is the cumulative frequency before the median class and c is the class size.
iii) Standard deviation = [tex]\sqrt{variance} = \sqrt{\frac{\sum{(f(x - \bar{x}))^2}}{\sum{f-1}} }[/tex],
iv) 1st quartile = L1 + {(n/4) - Cf}c
v) 3rd quartile = L3 + {(3n/4) - Cf}c
vi) Percentage of respondent having <3 siblings = number of those having <3 siblings/ n = 60 = (13+22)/60 = 35/60.
vii) 20% of all respondents have had at most how many siblings = 1 sibling.
