Level 1 Statistics

AS 1.5 (90---)

Use Statistical Methods and Information

Central Tendency

• Given a large set of data we need a single number that is descriptive of all the others.

• An average is a measure of a central value or central tendency and is meant to be typical of all values in a data set.

• The 3 averages used are • Mean• Median• Mode

Which average?

• Read page 264

Advantages and disadvantages of the mean, median and mode.

• You may wish to make a couple of quick notes for future reference.

• Do exercise 20.01 on page 264 start with numbers 4, 6, 7, and 8

Mean, Median & Mode Puzzle

• Only one number is less than the mean.There are five prime numbers.11 is not the only mode.The median is 11.The mean is 10.List the five numbers.

PUZZLE

• Edwards lowest possible score

On four tests, in which scores could be any whole number between 0 and 100, Edward had a mean score of 89. What is the lowest possible score Edward could have got on one of these tests?

Grouped Data

• Calculate the mean median and mode for the data given in this frequency table.

• Mean = • Median =• Mode =

Score (x) Frequency

3 2

4 4

5 4

6 7

7 3

8 4

9 1

a. In how many matches did the team score four goals?

b. What was the greatest number of goals scored in a match?

c. How many matches did the team play altogether?

d. Find the mean, median and mode number of goals the team scored?

GammaPage 269

Phone calls made by students last evening

• Calculate the mean median and mode for the data given in this frequency table.

• Mean = • Median =• Mode =

Calls Frequency

0 8

1 6

2 4

3 4

4 3

5 4

6 1

Shoe size

• Calculate the mean median and mode for the data given in this frequency table.

• Mean = • Median =• Mode =

Shoe Size Frequency

5 2

6 6

7 4

8 6

9 3

10 1

11 2

Last minute accommodation prices in Christchurch and Queenstown

Hotel/motel Thursday Friday Hotel/motel Thursday FridayMillbrook Resort 234 234 Crowne Plaza 169 169Mountvista Boutique Hotel 235 225 Aloha Motel 105 105Villa del Lago 295 295 Clearwater 240 240Blue Peaks Apartments 395 395 Greatstay 170 170Heritage Queenstown 169 395 Hotel off the Square 240 169Mercure St Moritz 160 160 Millennium 145 135Millennium 135 145 Camelot Cottages 150 150Nugget Point Resort 225 225 Centra 130 110Copthorne Lakefront 139 139 Chateau on the Park 149 149Hurleys of Queenstown 125 125 Copthorne 130 110Mercure Resort 105 105 Holiday Inn 115 115Novotel Gardens 145 145 Grand Chancellor 124 124Parkroyal 180 180 Rydges 125 115Whistler, the Chancellor 135 135 Fino Casementi 200 200Kingsgate 135 160 Kingsgate 99 99Rydges Queenstown 129 149 Sudima 99 99Sherwood Manor 85 85 The Manor 137 137

Queenstown Christchurch

95 95 33

95 234 25 25 2 00 4080 60 60 1 50 69 69 70

49 45 45 39 35 25 05 1 05 10 10 15 15 24 35 37 4985 0 99 99

0

Back to Back Stem and Leaf

Friday last minute accommodation prices

Queenstown Christchurch

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Group A Group B Group C

Questions

1. Which group has the highest median?

2. Which group has the largest range?

3. Which group has the lowest interquartile range?

4. 75% of Group ___ is above the median of Group ___.

5. If all three groups are the same size and the pass mark for the test is 60. Which group has the most that pass?

STARTER

Analysing Bivariate Data

• Two measurements associated with each member of the population.

– Eg: height & arm span for a class of students.

• A SCATTERPLOT is used to look at the relationship between the two measures.

Scatterplot

• When the question to be answered is something like:- Is there a relationship between price and mileage for a second hand car? – we use a scatterplot.

• The independent variable, (the one we have least control over) goes on the horizontal axis. This is often a time measurement.

• The dependent variable goes up the vertical axis.

• In the above example the price of a second hand car is likely to depend on the mileage so price would go vertical and mileage would go horizontal.

Analysing a scatterplot

• Look for positive or negative relationship.

• Look for a weak or strong relationship.

• Do the points fit a straight line, a linear relationship.

• Are there outliers, points that are far away from the others and don’t appear to fit the pattern?

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1011121314151617181920212223242526272829303132333435

A B CMEAN DAILY MINIMUM AIR TEMPERATURE (°C)Location Latitude Mean

minimum Kaitaia 35.2 11.8Whangarei 35.6 11.4Auckland 36.8 11.3Tauranga 37.6 10.0Hamilton 37.7 8.6Rotorua 38.2 8.2Gisborne 38.7 9.1Taupo 38.7 7.1New Plymouth 39.0 9.8Napier 39.5 9.6Wanganui 39.9 10.0Palmerston 40.3 9.1Masterton 41.0 7.4Wellington 41.3 9.9Nelson 41.3 7.8Blenheim 41.5 7.6Westport 41.7 8.8Kaikoura 42.4 9.0Hokitika 42.7 7.6Christchurch 43.6 7.2Mt Cook 43.6 3.7Lake Tekapo 44.0 3.4Timaru 44.4 6.5Milford Sound 44.6 6.1Queenstown 45.0 5.6Alexandra 45.2 4.9Manapouri 45.5 3.7Dunedin 45.8 7.5Invercargill 46.4 5.4Chatham Islands 44.0 8.8

Is there a relationship between latitude and mean daily minimum air temperature for New Zealand centres?

Plot latitude on the horizontal axis as we would predict temperature to depend on latitude.

Mean minimum temp at various NZ locations

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

32.0 37.0 42.0 47.0

Latitude

Tem

pera

ture

(d

eg

C)

Dishwasher prices and water use data

Price ($) Water Use (litres)$1,599 16$1,899 20

$950 18$2,199 19$1,199 19

$950 18$1,000 18$1,099 22$1,190 20

$900 20$999 11.5

$1,600 23$1,299 17

$900 22$1,099 20$1,199 21

$699 20$899 20

Moving Means - StarterMoving Means - Starter

The total rainfall in January was 7cm.

The mean rainfall for January, February and March was 5cm.

The mean rainfall for February, March and April was 3cm.

The mean rainfall for March, April and May was 3cm.

The mean rainfall for April, May and June was 2cm.

There was no rain in June.

What was the rainfall in each of the first 6 months of the year if the rainfall for all months was measured to the nearest cm?

What was the mean rainfall for the first 6 months of the year?

Time SeriesTime Series GraphsGraphs• Show a series of measurements recorded at specific

time intervals.• Time on the horizontal scale with regular intervals.• Measurements on the vertical scale.• Features

– Short term (Bus arrival example p295)• random fluctuations = noise.• marked differences = spikes or outliers.

– Long term (Ice cream sales example p296)

• general trend.• seasonal variations.

Exercise 21.03 p296, questions 1 to 5

Passengers using public transport in Wellington

YearNumber of

passengers (millions)

1933 36.01935 39.21937 44.01939 45.51941 50.01943 59.11945 61.61947 58.51949 55.71951 51.11953 44.71955 43.71957 39.01959 37.61961 36.11963 35.01965 33.11967 29.41969 26.71971 26.6

Passengers using public transport in Wellington

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1933

1935

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Year

Number of passengers

(millions)

Australian visitors

0100002000030000400005000060000700008000090000

Jan-

99

Mar

-99

May

-99

Jul-9

9

Sep-9

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9

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Monthly power bills

$0.00

$50.00

$100.00

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$200.00

$250.00

Jan

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aid