Question

Consider the following data: 3, 10, 8, 4, 5, 1 Compute (1) the sample standard derivation; (2) the sample median: (3) the IQR: and (4) draw a boxplot Please round your answer to the first decimal point.

Answer 1

The sample can be re written as

1, 3, 4, 5, 8, 10

1) To calculate sample standard deviation we need to find mean first using

$\bar{X}=\frac{\sum X_{i}}{n}=\frac{1+3+4+5+8+10}{6}=5.2$

Now sample standard deviation calculated as

$S=\frac{\sum (\bar{X}-X_{i})^{2}}{n-1}=\frac{(5.167-1)^{2}+(5.167-3)^{2}+...+(5.167-10)^{2}}{6-1}=3.3$

2) .The median is the center value of o any distribution if the distribution is in ascending order hence here,

(5+4)/2= 4.5 is the median.

3) IQR = Inter quartile range , it is calculated by first calculating 5 pint summary, so

Q1=3, Q2=4.5, Q3= 8 now IQR= Q3-Q1= 8-3=5

4. The box plot

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