Example 3 (Method 1 – Direct Method)
The distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. What does the mean signify?
Here Class Size is not same,
So, we solve by Direct Method
Mean(𝑥 ̅) = (∑▒𝑓𝑖𝑥𝑖)/(∑▒𝑓𝑖)
𝑥 ̅ = 6880/45
𝑥 ̅ = 152.89
Thus, Mean signifies that on average, 45 bowlers take 152.89 wickets
Example 3 (Method 2 – Step Deviation Method)
The distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. What does the mean signify?
Here Class Size is not same…
So, in Step Deviation Method
Mean(𝑥 ̅) = a + h × (∑▒𝒇𝒊𝒖𝒊)/(∑▒𝒇𝒊)
We use a value of h which can divide
𝑑𝑖 = 𝑥𝑖 − a
Mean(𝑥 ̅) = a + h × (∑▒𝒇𝒊𝒖𝒊)/(∑▒𝒇𝒊)
Where
a = Assumed Mean
Let h = Class interval
Also,
∑▒𝒇𝒊 = 45
∑▒𝒇𝒊𝒖𝒊 = −212
Putting values in formula
Mean(𝒙 ̅) = a + h × (∑▒𝒇𝒊𝒖𝒊)/(∑▒𝒇𝒊)
𝑥 ̅ = 200 + 10 × (−212)/45
𝑥 ̅ = 200 – 47.11
𝒙 ̅ = 152.89
Thus, Mean signifies that on average, 45 bowlers take 152.89 wickets

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.