Question

Find the 5 number summary of the following set of data:11, 8, 12, 4, 7, 10, 3, 15, 8, 8, 7 2.

Find the standard deviation (s) for the following: 8, 9, 8, 5, 6.

Answer 1

I assume the data set is 11, 8, 12, 4, 7, 10, 3, 15, 8, 8, 7, 2

if it is 11, 8, 12, 4, 7, 10, 3, 15, 8, 8, 72. then the same can be done.

From the given data set 11, 8, 12, 4, 7, 10, 3, 15, 8, 8, 7, 2

we arrange the dataser in ascending order as 2, 3, 4, 7, 7, 8, 8, 8, 10, 11, 12, 15.

the sample size is 12 and five point summary is the values calculating Minimum , Maximum, Q1, Q2, Q3

Q1 is the median of the first half data set and also the 25th percentile

Q2 is median of the complete dataset and also the 50th percentile value.

Q3 is the Median of the 2nd half of the data set and also the 75th percentile.

Now, finding the median first, since we have 12 no of values hence the middle value is somewhere between 6th and 7th value which is calculated as:

(8+ 8)/2

=8

Q1 is the median of first half so it lies between 3rd and 4th value as (4+7)/2=5.5

Q3 is the median of 2nd half so it lies between 9th  and 10 th value as (10+11)/2=10.5

Minimum=2

Maximum=15.

2). For this given data set 8, 9, 8, 5, 6

To find the standard deviation we need to find the mean first as:

Mean = (8 + 9 + 8 + 5 + 6)/5
= 36/5
Mean = 7.2

The Sample standard deviation is calculated as:

σ = √(1/5 - 1) x ((8 - 7.2)² + ( 9 - 7.2)² + ( 8 - 7.2)² + ( 5 - 7.2)² + ( 6 - 7.2)²)
= √(1/4) x ((0.8)² + (1.8)² + (0.8)² + (-2.2)² + (-1.2)²)
= √(0.25) x ((0.64) + (3.24) + (0.64) + (4.84) + (1.44))
= √(0.25) x (10.8)
= √(2.7)
= 1.6432