Part A: Measures of Central Tendency

Measures of central tendency (Mean, Median, and Mode) allow us to summarize a data set with a single representative value.

Problem 1: Livestock Management (Real-Life Application)

A pastoralist in Puntland records the daily milk yield (in liters) from a specific camel over a week: 8, 10, 7, 12, 10, 9, 14.

  1. Calculate the Mean daily milk yield:

  2. Identify the Mode of the data:

  3. Determine the Median yield:

Problem 2: Grouped Data Analysis

A local health clinic recorded the weights of 20 infants.

Weight Range (kg) Frequency (f) Class Midpoint (x) \(f \times x\)
2 – 4 4
4 – 6 8
6 – 8 5
8 – 10 3

Estimate the Mean weight:

Problem 3: Educational Study (Correlation)

A teacher wants to see if there is a relationship between the hours students spend studying (\(x\)) and their scores on a math test (\(y\)).

  1. If the points on the scatter diagram generally trend upward from left to right, what type of correlation is present?

[Image of a scatter plot showing positive correlation]

  1. If a student studies for 0 hours and still gets a high score, but another studies for 10 hours and gets a low score, causing no clear pattern, what is this called?

Problem 4: Market Prices

The prices of a 50kg bag of sugar in five different shops in Badhan are: $32, $35, $32, $38, and $33.

  • Question: Which measure of central tendency would be most affected if one shop suddenly increased its price to $60? Explain why.

Problem 5: Market Research

A shopkeeper records the daily number of customers over a month. Find the Mode for the following distribution:

Number of Customers Frequency (f)
10 – 20 5
20 – 30 12
30 – 40 8
40 – 50 5

Problem 6: Student Heights

The heights of 40 students in a Form Three class were recorded. Calculate the Median height.

Height (cm) Frequency (f) Cumulative Frequency (\(Cf\))
140 – 150 6 6
150 – 160 14 20
160 – 170 15 35
170 – 180 5 40

End of Assignment