Question

Quantitative

Problems 2 through 7 refer to the following 20-point data set.

{7, 12, 18, 25, 1, 13, 25, 9, 6, 9, 2, 14, 24, 13, 14, 11, 6, 8, 27, 19}

2.

Construct a histogram using an interval width of 5.

3.

Using the data, calculate the mean, mode, median, and midrange

4.

Using the histogram, describe the shape of the distribution.

5.

What percentage of the data are greater than the mean?

6.

Using the data, calculate the range, standard deviation, and inner quartile range

(IQR).

7.

Identify any outliers in the data and explain why, i.e., greater than 2 standard

deviations from the mean from the mean.

Answer 1

From the given data(in ascending order):

1,2,6,6,7,8,9,9,11,12,13,13,14,14,18,19,24,25,25,27

(2) Histogram plot:

(3) Mean(x-bar)=Xi/n=263/20=13.15

Median=(10th+11th)/2=(12+13)/2=12.5

This is multi model data

Mid range=(max+min)/2=(27+1)/2=14

(4) This is right skewed data as we can see mean is larger than the median in the above histogram plot.

(5)here we have

k=12(number of data smaller than 13.15) ,n=20

so percentile rank=12/20=0.60

i.e. 60%

(6)From the given data

range=max-min=27-1=26

Sample standard deviation (s)=7.707

Median=12.5
Minimum= 1
Maximum= 27
First quartile= 7.25
Third quartile= 18.75
Interquartile Range=3rd quartile-1st quartile=18.75-7.25= 11.5

(7) Here standard deviation is 7.707

data larger than two standard deviation from the mean is 13.15+2*7.707=28.564

There is no data larger than 28.564 hence we can say there is no outlier.