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 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

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? Gamma Page 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 = CallsFrequency

Shoe size Calculate the mean median and mode for the data given in this frequency table. Mean = Median = Mode = Shoe SizeFrequency

Back to Back Stem and Leaf Friday last minute accommodation prices QueenstownChristchurch

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?

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.

Moving 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?

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 p296, questions 1 to 5