Question

1. Given the following set of grades from a recent statistics exam:

92	88	93	95	94
89	88	78	77	76
77	74	72	68	54
99	94	91	85	84
88	34	56	87	82

a) (5 points) Sketch the histogram of the data.  You may either sketch it by hand or give a screenshot of Statkey.

b) (6 points) Describe the shape of the data. Describe the modality, symmetry, and any unusual features, e.g., outliers.

c) (5 points) State the Five Number Summary of the data, including labeling what each number represents.

d) (4 points) State the best measure for the center and spread. Explain your answers.

Answer 1

a)

Histogram

b)

Modality: Unimodal (since there is only one peak.)

Symmetry: Skewed Left

Outliers: 34 is the outlier

c) Using Excel<data<megastat<descriptive statistics

Here is the output:

Descriptive statistics
	# 1
count	25
mean	80.60
sample standard deviation	15.03
sample variance	225.83
minimum	34
maximum	99
range	65
1st quartile	76.00
median	85.00
3rd quartile	91.00
interquartile range	15.00
mode	88.00
low extremes	0
low outliers	1

Five number summary

Minimum 34

First quartile 76

Median 85

Third Quartile 91

Maximum 99

d) The best measure for the center and spread, I would say the median as an outlier will affect the mean by a lot, while the median won't be affected as much. However, if terms near the median without the outlier have high variation, then using a mean may be better.