60 randomly selected students were asked how many siblings were in their family. let x = the number of pairs of siblings in the student's family.
the results are as follows:

siblings frequency
1 13
2 22
3 15
4 6
5 3
6 0
7 1

round your answers to two decimal places.
1. the mean is
2. the median is
3. the sample standard deviation is
4. the first quartile is
5. the third quartile is

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

can you add an image ?

step-by-step explanation:

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: