Question

1. Four coins are tossed 11 times. The number of heads is counted and the following data is reported: 4, 3, 2, 0, 3, 3, 1, 2, 3, 2, 1.

Calculate the following sample statistics. Be sure to provide a formula for your answer.

a. Sample mean?

b. Sample median?

c. Sample mode?

d. Sample range?

e. Sample variance?

Answer 1

X = No of heads

X - 4, 3, 2, 0, 3, 3, 1, 2, 3, 2, 1

(a) Sample mean = sum of all terms / number of terms

Sum of all terms = 4+ 3+2+0+3+3+1+2+3+2 +1 =24

number of terms = 11

sample mean = 24/ 11 = 2.182

(b) sample median

The median is the middle number in a sorted list of numbers. We need to place the numbers in value order and find the middle number.

Data in ascending order: 0   1   1   2   2   2   3   3   3   3   4  

There are 11 observations so the 6th observation is the sample median = 2

(c) sample mode

The mode of a set of data is the value in the set that occurs most often.

in the data: 0 and 4 occur 1 time, 1 occurs 2 times, 2 occurs 3 times and 3 occurs 4 times

Hence 3 is the sample mode

(d) sample range

The range is the difference between the highest and lowest values in the data set.

The lowest value is 0.

The highest value is 4.

Sample range = 4 - 0 = 4.

(e) sample variance:

Create below table

data	data-mean	(data - mean)2
4	1.8182	3.30585124
3	0.8182	0.66945124
2	-0.1818	0.03305124
0	-2.1818	4.76025124
3	0.8182	0.66945124
3	0.8182	0.66945124
1	-1.1818	1.39665124
2	-0.1818	0.03305124
3	0.8182	0.66945124
2	-0.1818	0.03305124
1	-1.1818	1.39665124

sample variance = 1.3636