MODULE 5 – MEASURES OF CENTRAL TENDENCY
MEASURES OF CENTRAL TENDENCY
EXAMPLE:
Describes a set of data by identifying the
central position in the data set as a single
value.
MEAN
, the average of a set of data.
MEDIAN
, the middle value when all the elements
in a set of data are arranged in ascending
or descending order.
23(45)
100
𝐏𝟐𝟑 = 𝟏𝟎. 𝟑𝟓
P23 =
MODE
, the element in a set of data that has
the most number of frequencies.
QUANTILES
These are statistics that describe various
subdivisions of a frequency distribution
into equal proportions.
PERCENTILES
These are 99 values that split data in 100
equal parts.
P1 P2 P3 … P99
FORMULA:
𝐤𝐍
𝐪
𝐿𝑘 – location of the 𝑘𝑡ℎ quantile element
𝑘 – the order of a quantile (P32 , 𝑘 = 32)
𝑞 – type of quantile (P32 , 𝑞 = 100)
𝐋𝐤 =
𝐤𝐍
− < 𝐜𝐟𝐛
𝐪
𝒒𝒌 = 𝐗𝐋𝐁 + 𝐢 (
)
𝐟𝐪𝐤
𝑋𝐿𝐵 – lower boundary of the quantile class
𝑖 – class size
𝑞 – type of quantile
𝑓𝑞𝑘 – class frequency of quantile class
< 𝑐𝑓𝑏 – less than cumulative frequency
before the quantile class
1
10.35 − 6
P23 = 25.5 + 5 (
)
5
𝐏𝟐𝟑 = 𝟐𝟗. 𝟖𝟓