Measures of dispersion

Question 1

Describe the red, blue and black line

Answer 1

Red- low variability ( condensed around the mean)

Blue - medium variability

Green - high variability ( the data is spread out around the mean)

Question 2

What does variance measure?

Answer 2

How spread out a set of numbers are from the mean.

Question 3

How do we calculate sample variance?

Answer 3

1) Find the mean of the dataset
2) Find the difference of each observation from the mean
3) Take the square differences of each difference
4) Add up all squared differences
5) Divide by n-1

Question 4

How can we show sample variance is notation form?

Answer 4

Question 5

Calculate sample variance

Answer 5

Question 6

Whats another way to calculate sample variance?

Answer 6

Question 7

How do we find sample variance of a frequency table?

Answer 7

1) Calculate the mean ( summation of midpoint x frequncy divide by n)
2) find square differences which is ( midpoint - mean)^2
3) Multiply square differences by corresponding frequency
4) Add up the mutiple of square differences and corresponding frequency
5) divide by n-1

Question 8

What is the notation of variance for a frequency table?

Answer 8

Question 9

Calculate mean, sample variance and SD?

Answer 9

Question 10

What is a disdvantage of sample variance?

Answer 10

Different units of measurement

Question 11

What methods solves the problem of different units of measurement and how do we work it out?

Answer 11

Standard deviation and its the square root of the variance.

Question 12

What does standard deviation mean?

Answer 12

Measures how spreaded out the data is from the mean.

Question 13

If a question says find 1,2 and 3 standard deviations from the mean how do we do this?

Answer 13

Question 14

Answer 14

Question 15

What is range and what is a disadvantage of it?

Answer 15

Max - Min and its affected by outliers

Question 16

What is the Interquartile range?

Answer 16

Interquartile range measures variability by dividing the data into quartiles/quarters.

Question 17

Lets say n =10

62 63 64 64 70 72 76 77 81 81

Find IQR

Answer 17

Question 18

If sample size is odd,= 9

63 64 64 70 72 76 77 81 81

What is the IQR

Answer 18

Question 19

What do histograms allow us to do?

Answer 19

Histograms help us visualise the centre and variability in a data set

Question 20

Which histogram would have the biggest SD?

Answer 20

The last one

Question 21

What are the 5 things a box plot must always contain?

Answer 21

Minimum value, lower quartile, median, upper quartile and maxmium value.

Question 22

What does the whiskers of the box plot extend too?

Answer 22

The whiskers extend on either side of the box to: 1.5 x IQR the minimum value that is within of the lower quartile, 1.5 X IQR the maximum value that is within of the upper quartile.

All data outside the whiskers are outliers, represented by points.

Question 23

Construct a box plot

Answer 23

Question 24

Answer 24

Question 25

With box plots what can you do to compare with other box plots?

Answer 25

Look at the variability

Look at the highest and lowest value

Look at the median value

Question 26

Question 3

You have a sample of 9 observations of weights (in kg), with mean of 65kg. You are then given a 10^th observation and the new mean is 68kg. What is the value of the 10^th observation?

Answer 26

Question 27

Answer 27