Answer:
1. mean=2.47
2. median=2
3. Sample Standard deviation=1.24
4. First quartile=2
5. Third quartile=3
Step-by-step explanation:
The necessary calculations for finding mean,median,standard deviation, 1st quartile and 3rd quartile are
sumf=13+22+15+6+3+0+1=60
sumfx=13*1+22*2+15*3+6*4+3*5+0*6+1*7=148
sumfx²=13*1²+22*2²+15*3²+6*4²+3*5²+0*6²+1*7²=456
x cumulative frequency
1 13
1 23+22=35
3 35+15=50
4 50+6=56
5 56+3=59
6 59+0=59
7 59+1=60
1.
mean=sum(fx)/sumf
Here x is number of siblings and f is frequency
mean=148/60=2.4667
So, after rounding to two decimal places our mean is 2.47.
2.
Median=value of (n/2)th observation
Median=value of (60/2)th observation
Median=value of 30th observation
The cumulative frequency shows that the 30th observation corresponds to x=2 sibling. So, the median is 2.
3.
s=1.2415=1.24
4.
1st quartile=Q1=((n+1)/4)th values of observation
Q1=((61)/4)th values of observation
Q1=(15.25)th values of observation
15.25th value also corresponds to x=2 siblings so,
Q1=2.
5.
3rd quartile=Q3=(3(n+1)/4)th values of observation
Q3=(3(61)/4)th values of observation
Q3=(45.75)th values of observation
45.75th value corresponds to x=3 siblings so,
Q3=3