Topic 1 Stats

8/13/2019 Topic 1 Stats

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STATISTICS!!!

The science of data

What is data?

Information, in the form of facts orfigures obtained from experiments

or surveys, used as a basis for

making cacuations or draing

concusions

"ncarta dictionary


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Statistics in Science

# $ata can be coected about apopuation %surveys&

# $ata can be coected about a

process %experimentation&

' types of $ata

(uaitative

(uantitative


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(uaitative $ata

# Information that reates to characteristics ordescription %observabe )uaities&

# Information is often grouped by descriptivecategory

# "xampes* Species of pant

* Type of insect

* Shades of coor

* +ank of favor in taste testing

Remember: qualitative data can be scored andevaluated numerically

(uaitative data, manipuated

numericay# Survey resuts, teens and need for environmenta action


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(uantitative data

# (uantitative * measured using a

naturally occurring numerica scae# "xampes

*Chemica concentration

*Temperature

*ength

*Weight-etc.

(uantitation

# /easurements are often dispayedgraphicay


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(uantitation 0 /easurement

# In data coection for 1ioogy, data must bemeasured carefuy, using aboratory e)uipment

%ex. Timers, metersticks, p2 meters, baances , pipettes, etc The imits of the e)uipment used add some

uncertainty to the data coected. A e)uipmenthas a certain magnitude of uncertainty. 3orexampe, is a ruer that is mass4produced agood measure of 5 cm? 5mm? 6.5mm?

# 3or )uantitative testing, you must indicate thelevel of uncertainty of the tool that you areusing for measurement!!

2o to determine uncertainty?

# 7suay the instrument manufacturer i indicate

this * read hat is provided by the manufacturer.

# 1e sure that the number of significant digits in

the data tabe8graph refects the precision of the

instrument used %for ex. If the manufacturer

states that the accuracy of a baance is to 6.5g *

and your average mass is '.69g, be sure to

round the average to '.5g& :our data must be

consistent ith your measurement tooregarding significant figures.


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3inding the imits

# As a ;rue4of4thumb degreesC, ith a thermometer that is scored at 5 degreeintervas * hat is the range of possibetemperatures for the room?

# %ans.s =84 6.> degrees Cesius 4 if you read5>oC, it may in fact be 5.> or 5>.> degrees&

ooking at $ata

# 2o accurate is the data? %2o cose arethe data to the ;rea< resuts?& This is aso

considered as 1IAS

# 2o precise is the data? %A test systems

have some uncertainty, due to imits of

measurement& "stimation of the imits of

the experimenta uncertainty is essentia.


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Comparing Averages

# @nce the ' averages are

cacuated for each set of data,the average vaues can be potted

together on a graph, to visuaie

the reationship beteen the '


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$raing error bars

# The simpest ay to dra an error bar is touse the mean as the centra point, and to

use the distance of the measurement that

is furthest from the average as the

endpoints of the data bar


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Average

vaue

Baue farthest

from average

Cacuateddistance

What do error bars suggest?

# If the bars sho extensive overap, it is

ikey that there is nota significant

difference beteen those vaues


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(uick +evie * measures of

;Centra Tendency percent of the data.


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Three Standard $eviations?

# three standard deviations %the red, green

and bue areas& account for about JJpercent of the data

4sd 4'sd =845sd 'sd =sd

2o is Standard $eviation

cacuated?

With this formua!


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Basic example of Calculating Standard Deviation

Consider a population consisting of the following values

"here are eight data points in total, with a mean (or average) value of /%

"o calculate the standard deviation, we compute the difference of each data point from the mean, and

s6uare the result%

7et we average these values and ta!e the s6uare root, which gives the standard deviation%

"herefore, the population above has a standard deviation of 2.


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1. 5hat is meant by the following terms8

a. 9ean

b. Standard deviation

c. :ange; variability

2. Error bars can be used to show variability in data (either range of data or standard deviation)


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&. 4n the aes below, plot the following three curves (all have a normal distribution)%

a. >as the highest mean and a high standard deviation.

b. >as the lowest mean, but the highest fre6uency at that mean.

c. >as a mean between (a) and (b) and has the smallest standard deviation.

0. Complete the following statements by either filling in the blan! or circling the correct answer;

a) 1- (standard deviation) from the mean represents * of all the data points.

b)


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. Calculate the means and standard deviations of these two

groups of data (to one decimal place)

Show your wor!ing here.

$.


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Boo! at the graph below%

. 5hich of the following statements are true8

a. "here is no correlation between number of cellphones and number of students with asthma.

b. "here is a positive correlation between number of cellphones and asthma cases.

c. "here is a negative correlation between number of cellphones and asthma cases

d.

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Topic 1 Stats