UNIT 3: Summarising data: measures of central tendency and dispersion

Question 1

Median from discrete data

Answer 1

To find the middle of the list for n numbers you find the (n+1)/2 th value

Question 2

Negative Skew

Answer 2

• peak on the right
• toes on left feet
• mean

Question 3

Symmetric

Answer 3

• peak in the middle

- mean=median=mode

Question 4

Positive Skew

Answer 4

• peak on the left
• toes on right feet
• mean>median>mode

Question 5

Geometric Mean

Answer 5

nth root of value 1 * value 2 * … * value n

Question 6

When to use the geometric mean

Answer 6

• When you are finding an average of percentage increase/decrease or RATES.
• When you are comparing things that have several very different values. Eg marks out of 100 and marks of out 10 for each item

Question 7

Weighted Mean

Answer 7

∑weight

Question 8

Which measure of spread to compare for MODE

Answer 8

Range

Question 9

Which measure of spread to compare for MEDIAN

Answer 9

Interquartile range (or if specified in the question the inter percentile range)

Question 10

Which measure of spread to compare for MEAN

Answer 10

Standard Deviation

Question 11

Advantages of Range

Answer 11

Easy to calculate

Question 12

Disadvantages of Range

Answer 12

Affected by outliers

Question 13

Advantages of IQR/Inter decile/percentile range

Answer 13

Not affected by outliers

Question 14

Disadvantages of IQR/Inter decile/percentile range

Answer 14

Doesn’t allow you to calculate skew

Question 15

Advantages of standard deviation

Answer 15

Use to calculate skew

Question 16

Disadvantages of standard deviation

Answer 16

Affected by outliers

Doesn’t have much meaning for skewed data

Question 17

Advantages of mean

Answer 17

• Uses all the data
• Use to calculate standard deviation
• Use to calculate skew

Question 18

Disadvantages of mean

Answer 18

-Always effected by extreme values
-Hard to calculate if you have an open ended class in a table.
(eg x>300)

Question 19

Advantages of mode

Answer 19

• Easy to find (calculate)
• Can always find the mode - even for qualitative data
• Not affected by extreme values
• Always a data value in the set

Question 20

Disadvantages of mode

Answer 20

• May be no mode
• May be more than one mode
• Cannot use it to calculate a measure of spread

Question 21

Advantages of median

Answer 21

• Easy to calculate (Unless using interpolation)
• Not affected by extreme values
• Best to use when data is skewed
• Can be used to calculate IQR and skew and outliers

Question 22

Disadvantages of median

Answer 22

May not be a data value