Question

76		Statistic
64		Sample Size
62		Sample Mean
81		Sample Standard Deviation (SD)
70
72		Minimum
81		First Quartile (Q1)
63		Median (Q2)
67		Third Quartile (Q3)
77		Maximum

Answer 1

Sample size is 10

Sample mean is

Sample Standard deviation is calculated as below

Create the following table.

data	data-mean	(data - mean)2
76	4.7	22.09
64	-7.3	53.29
62	-9.3	86.49
81	9.7	94.09
70	-1.3	1.69
72	0.7	0.49
81	9.7	94.09
63	-8.3	68.89
67	-4.3	18.49
77	5.7	32.49

Find the sum of numbers in the last column to get.

So

The minimum is the smallest value in a data set.

Ordering the data from least to greatest, we get:

62   63   64   67   70   72   76   77   81   81   

So, the minimum is 62.

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

62   63   64   67   70   72   76   77   81   81   

So, the bottom half is

62   63   64   67   70   

The median of these numbers is 64.

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

Ordering the data from least to greatest, we get:

62   63   64   67   70   72   76   77   81   81   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median=

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

62   63   64   67   70   72   76   77   81   81   

So, the upper half is

72   76   77   81   81   

The median of these numbers is 77.

The maximum is the greatest value in a data set.

Ordering the data from least to greatest, we get:

62   63   64   67   70   72   76   77   81   81   

So, the maximum is 81.