Question

Use the data from problem:

52.2 43.8 50.3 51.1 48.3 47.8 48.3 47.4 50.1 50.5 51.4 54.2 54.4 48.6 54.5 47.3 50.3 48.1 46.6 50.2 50.5 48.2 46.3 48.1 49.4 50.5 47.7 50.1 45.6 49.3 44.4 47.2 47.6 56.9 48.9 49.9 46.3 44.9 51.2 48.5 49.2 46.6 47.3 45.3 49.2 51.1 49.2 50.0 49.8 48.2 47.2 42.6 46.9 46.5 47.3 46.5 47.7 49.2 46.3 48.5 53.4 48.0 50.0 49.7 48.8 48.3 48.7 48.1 48.2 48.6 48.3 48.3 48.3 48.3 48.6 48.2 48.3 48.7 48.1 48.5

a. Calculate the sample mean, sample median, sample variance, and sample standard deviation.
b. Construct a Stem and Leaf Plot, Histogram, and Box Plot.

Answer 1

a) Sample mean: 48.71

Sample median: 48.3

Sample variance: 5.41

Sample standard deviation: 2.37

Explanation:

a) Sample mean:

`\bar{X}=(1)/(N) \sum X_i=(1)/(80)*3896.9=48.71`

Sample median: M=48.3

Note: I order the data increasingly and take the value N / 2 = 40. In this way there are 39 values above and 39 values below the median.

Sample variance:

`s^2=(1)/(N-1)\sum (X_i-\bar X)^2 =((1)/(80-1))*427.74=5.41`

Sample standard deviation

`s=√(s^2)=√(5.41)=2.37`

b)