interpreting numerical summaries

Question 1

mean

Answer 1

the average or ‘typical’ value of a dataset

Question 2

median

Answer 2

the midpoint, separating to lower 50% with the upper 50% of the ordered data

• > odd dataset - the middle number
• > even dataset - the average of the 2 middle numbers (A+B)/2

Question 3

mode

Answer 3

the most common value(s) in a dataset

Question 4

symmetry

Answer 4

degree to which the distribution looks like a mirror image when split down the centre

Question 5

modality

Answer 5

the number of prominent (import) peaks in the distribution

Question 6

skewness

Answer 6

the degree to which one tail of a distribution is spread farther than the other

• > if data is spread out more towards the right, its referred as right-skewed (mean is more than median)
• > if data is spread out more towards the left, its referred as left-skewed (mean is less than median)

Question 7

data of measure of spread

Answer 7

jennifer’s data is inconsistent

harry’s data is consistent

both have similar means

Question 8

range

Answer 8

difference between maximum and minimum values

Question 9

problem with range

Answer 9

the maximum or minimum values of the data are usually very off from the main data

could give misleading picture or graph of data

Question 10

variance and standard deviation

Answer 10

the ‘average’ distance between values and the mean

1) mean is calculated
2) difference from mean is taken
3) square each difference from mean values
4) add up the square differences then divide by n-1, gives variance (unit²)
5) then square root gives the standard deviation

Question 11

percentiles and quartiles

Answer 11

percentile a value below which a particular percentage of a distribution lies

quartiles divided the distribution into 4 equal-sized groups

Q1: 25th percentile

Q2: 50th percentile (median)

Q3: 75th percentile

Question 12

finding quartiles

Answer 12

split the ordered data in half (median)

find the median of the lower half or the upper half

the median of the lower half or upper half is the quartile

for an odd number of values, include the median in both halves

for an even number of values, split the distribution into equal-sized halves

Question 13

five-number summary

Answer 13

• > minimum
• > median (centre of the distribution)
• > maximum
• > Q1
• > Q3

interquartile range IQR = Q3 - Q1, to find the range of the middle 50%

Question 14

interquartile range (IQR)

Answer 14

Q₃ - Q₁ = interquartiler range (IQR)