1. Statistics 1: Statistical Measures
Pearson: Chapter 9.1 p279 – 283; 9.2 p288 – 291
Homework: Exercise 9.1 Q10 a,b
Exercise 9.2 p306 Q2, 5, 6
Haese & Harris: Chapter 20 p501 – 517,
Homework: Ex 20A Q4 Ex 20B.1 Q 5, 9, 12 Ex 20B.2 Q3 Ex 20B.3 Q Ex 20D Q1, 2

2. Basic Definitions
Using the GDC: (see “using the GDC” on Moodle for more help with Ti84 and TiNspire)
Discrete Data:
Press STAT and then 1:Edit;
Enter values into L1 (frequencies in L2)
Press STAT > CALC, 1:1-var stats
List = L1; FreqList is either blank or L2,
mean, median, standard deviation,
Q1, Q3, max, min are displayed
Grouped Data:
Press STAT and then 1:Edit;
Enter midpoint values into L1 (frequencies in L2)
Press STAT > CALC, 1:1-var stats
List = L1; FreqList is either blank or L2,
mean is an ”estimate”, median & quartiles will be incorrect

3. Measures of Central Tendency𝑥
In a frequency table, the mean is the sum of the frequency x data value ÷ total number
For grouped data, the midpoint of the interval x frequency ÷ total number
gives an estimate of the mean. (do not use your GDC to calculate the median of grouped data)

4. Measures of Central Tendency
1. Calculate the mean, mode and median of this data.
2. The table shows the scores of competitors in a competition.
The mean score is 34. Find the value of k. 3.

5. Histograms
Histograms are a frequency graph for grouped (usually continuous) data.
There are no gaps between the bars. The data can be entered into the GDC by using the midpoints of each interval for “x”.
4. The histogram to the right shows the house prices in thousands of Australian dollars (AUD) of a random sample of houses in a certain town in Australia.
(a) How many houses are there in the sample?
Write down the modal group for house prices.
Calculate an estimate for the mean.
(c) Find the probability of choosing a house at random which costs less than AUD or more than AUD.
(d) Given that a house costs more than AUD, find the probability that it costs between and AUD.

6. Measures of Spread Box & Whisker Plots
Range = the maximum value – the minimum value
Lower or First Quartile (Q1) = the first 25% of the ordered data. It is the median of the values below the median. Often called the 25th percentile.
Median or Second Quartile (Q2) = the first 50% of the ordered data. Often called the 50th percentile.
Upper or Third Quartile (Q3) = the first 75% of the ordered data. It is the median of the values above the median. Often called the 75th percentile.
Interquartile Range = Q3 – Q1 = the middle 50% of the data
Box & Whisker Plots
A visual representation of the “5 number summary” found on the GDC.
Each section represents 25% of the data
When drawing one, rule the lines & the whiskers do not pass through the box.

7. Box & Whisker Plots
5. A boxplot has been drawn to show the distribution of marks (out of 100) in a test for a particular class.
6. The following diagram is a box and whisker plot for a set of data.
The interquartile range is 20 and the range is 40.
Write down the median value.
Find the value of a b
What was the i) highest mark
ii) lowest mark scored?
What was the median test score for the class?
What was the range of marks scored for this test?
What percentage of students scored 60% or more for the test?
What was the interquartile range for this test?
The top 25% of students scored a mark between
______ & ______
If you scored 70 for this test, would you be in the top 50% of students in the class?

8. Outliers & Box and Whisker Plots
Outliers are values that are much smaller or larger than the other values.
Outliers are defined as being more than 1.5 x IQR from the nearest quartile
Outliers are represented on a box and whisker plot by a *, so the “minimum” or “maximum” value is the smallest or largest value within 1.5 x IQR. It is possible to more than one outlier.
7. Test the following data for outliers and hence construct a boxplot for the data: