Question

6. The following set of data is from a sample of n=10)
7 4 9 7 12 8 10 15 7 9

a. Compute the mean, median, and mode.
b. Compute the first, second and third quartiles.
c. Compute the range, variance, standard deviation, and coefficient of variation
d. Compute the Z scores. Are there any outliers?

Answer 1

Answer on Question #46343 - Math - Statistics and Probability

6. The following set of data is from a sample of $n=10$)

7 4 9 7 12 8 10 15 7 9

a. Compute the mean, median, and mode.

b. Compute the first, second and third quartiles.

c. Compute the range, variance, standard deviation, and coefficient of variation

d. Compute the Z scores. Are there any outliers?

Solution

a. The mean is 8.8

The median is 8.5

The mode is 7 (the most common number).

R code:

c <- c(7,4,9,7,12,8,10,15,7,9)

mean(c)

median(c)

b. The first quartile is 7.5

The second quartile is 8.5

The third quartile is 9.75

R code:

quantile(c)

c. Compute the range, variance, standard deviation, and coefficient of variation

The range is 4-15

The variance is 9.29

The standard deviation is 3.05

The coefficient of variation is $34.63\%$

R code:

range(c)

var(c)

sd(c)

$100 \times \frac{sd(c)}{mean(c)}$

d. Compute the Z scores. Are there any outliers?

There are no outliers because there are no z-scores greater than 3 or less than -3. Value 15 is a

potential outlier with z-score more than 2.

R code:

z <- format((c - mean(c))/sd(c), digits=1)

cbind(c,z)

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