Course:FRST 231 DE/Statistical Measures and Tools of Descriptive Statistics

This quiz is designed to help you practice and gain confidence with Module 1 of FRST 231. For each question below, do your best to solve it on your own, then click 'Submit' to see the correct answer as well as an explanation.

The topics covered in this quiz include:

Using raw data to create frequency distributions
Analyzing different types of frequency distributions
Sturge's rule
Measures of central tendency and variability
Chebyshev's theorem

The Coast redwood (Sequoia sempervirens) is the tallest species of tree in the world.

According to Wikipedia, there are 28 species of tree which have achieved heights over 80m. These are given below, alongside the height of the tallest observed specimen from each species.


Tree species	Maximum height (m)	Tree species	Maximum height (m)
Lawson cypress (Chamaecyparis lawsoniana)	81.08	Karri (Eucalyptus diversicolor)	85.00
Shorea gibbosa	81.11	Mengaris (Koompassia excelsa)	85.76
Grand fir (Abies grandis)	81.40	Alpine ash (Eucalyptus delegatensis)	87.90
Entandrophragma excelsum	81.50	Dinizia excelsa	88.50
Sydney blue gum (Eucalyptus saligna)	81.50	Brown top stringbark (Eucalyptus obliqua)	88.50
Ponderosa pine (Pinus ponderosa)	81.77	Noble fir (Abies procera)	89.90
Shorea smithiana	82.27	Southern blue gum (Eucalyptus globulus)	90.70
Shorea johorensis	82.39	Manna gum (Eucalyptus viminalis)	92.00
Hopea nutans	82.82	Giant sequoia (Sequoiadendron giganteum)	96.30
Western hemlock (Tsuga heterophylla)	83.34	Sitka spruce (Picea sitchensis)	96.70
Sugar pine (Pinus lambertiana)	83.45	Coast Douglas-fir (Pseudotsuga menziesii var. menziesii)	99.70
Shining gum (Eucalyptus nitens)	84.30	Mountain ash (Eucalyptus regnans)	100.50
Shorea superba	84.41	Yellow meranti (Shorea faguetiana)	100.80
Shorea argentifolia	84.85	Coast redwood (Sequoia sempervirens)	115.92

You can download the dataset as an excel file here.

Question 1

Question 2

Question 3

The below table provides a frequency distribution using six classes for the tall tree dataset. The table is incomplete because a number of values (bold letters) are missing.


Class number	Lower class limit	Upper class limit	Lower class boundary	Upper class boundary	Class Mark	Frequency
1	81.08	86.88	81.075	86.885	83.98	16
2	86.89	A	86.885	92.695	89.79	B
3	C	98.50	D	98.505	95.60	2
4	98.51	104.31	98.505	E	F	3
5	104.32	110.12	104.315	110.125	107.22	G
6	H	I	J	K	L	M

Question 4

Question 5

The giant sequoia (Seqoiodendron giganteum) is the 6^th tallest tree in the world by, but the largest tree by mass.

What are the relative, cumulative, relative cumulative, inverse cumulative, and relative inverse cumulative frequencies of class 3?

HINT: round to two decimal places for relative frequencies, but use whole numbers for the others.

Question 6

What are the relative, cumulative, relative cumulative, inverse cumulative, and relative inverse cumulative frequencies of class 6?

HINT: round to two decimal places for relative frequencies, but use whole numbers for the others.

Question 7

The following histogram shows the frequency distribution for the tree heights dataset, using the class limits and number of classes from earlier questions.

Question 8

The following polygon shows the cumulative frequency distribution for the tree heights dataset, using the class limits and number of classes from earlier questions. The data labels display the cumulative frequency for each class.

Question 9

The following polygon shows the relative inverse cumulative frequency distribution for the tree heights dataset, using the class limits and number of classes from earlier questions. The data labels display the relative inverse cumulative frequency for each class.

Question 10

Question 11

The Douglas fir (Pseudotsuga menziesii) is the 5^th tallest tree species in the world, and the tallest of Canada's native tree species.

Question 12

Question 13

Select all the correct formulae that are used to calculate population variance ( $\sigma ^{2}$ ) or sample variance ( $s^{2}$ ) for raw data. (Note that $x_{i}$ represent individual tree heights and ${\bar {x}}$ or $\mu$ are mean tree height.)

	$s^{2}={\frac {\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}{n-1}}$
	$s^{2}={\frac {\sum _{i=1}^{n}(x_{i}-{\bar {x}})}{n}}$
	$\sigma ^{2}={\frac {\sum _{i=1}^{N}(x_{i}-\mu )^{2}}{N}}$
	$\mu ={\frac {\sum _{i=1}^{N}x_{i}}{N}}$
	$s^{2}={\frac {\sum _{i=1}^{n}x_{i}^{2}-{\frac {(\sum _{i=1}^{n}x_{i})^{2}}{n}}}{n-1}}$
	$s={\sqrt {\frac {\textstyle \sum _{k=1}^{n}\displaystyle (x_{i}-{\bar {x}})^{2}}{n-1}}}$

Question 14

Select all the correct formulae that are used to calculate population variance ( $\sigma ^{2}$ ) and sample variance ( $s^{2}$ ) for grouped data (i.e. from a frequency distribution). (Note that $x_{i}$ represent individual tree heights, ${\bar {x}}$ or $\mu$ are mean tree height, and $m_{i}$ are class marks.)

	$s={\sqrt {\frac {\sum _{i=1}^{n}f_{i}(m_{i}-{\bar {x}})^{2}}{n-1}}}$
	$s^{2}={\frac {\sum _{i=1}^{n}f_{i}(m_{i}-{\bar {x}})^{2}}{n-1}}$
	$\sigma ^{2}={\frac {\sum _{i=1}^{N}m_{i}^{2}f_{i}-{\frac {(\sum _{i=1}^{N}m_{i}f_{i})^{2}}{N}}}{N}}$
	$s^{2}={\frac {\sum _{i=1}^{n}m_{i}^{2}f_{i}-{\frac {(\sum _{i=1}^{n}m_{i}f_{i})^{2}}{n}}}{n-1}}$
	$s^{2}={\frac {\sum _{i=1}^{n}m_{i}^{2}f_{i}-{\frac {(\sum _{i=1}^{n}m_{i}f_{i})^{2}-{\frac {\sum _{i=1}^{n}m_{i}f_{i}^{2}}{n}}}{n}}}{n-1}}$

Question 15

Question 16

Question 17

Question 18

Question 19

FRST 231 wiki quizzes created by Suborna Ahmed and Spencer Shields. Permission is granted to copy, distribute and/or modify this document according to the terms in Creative Commons License, Attribution 4.0 International . The full text of this license may be found here: CC by 4.0

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