Question

Show that the mode of the series obtained by the combining two series s1 and s2 given below is different from that s1 and s2 taken separately.

S₁ : 3, 5, 8, 8, 9, 12, 13, 9, 9
S₂ : 7, 4, 7, 8, 7, 8, 13

Answer 1

The mode of S₁ is 9, and the mode of S₂ is 7. After combining these two series, the combined series has two modes: 7 and 9, each appearing four times. Thus, the mode has changed when the two series are combined.

Step-by-step explanation:

The question requires us to show that the mode of two separately given series, S₁ and S₂, changes when we combine them into one series. Let's first find the mode of each series separately:

• S₁: 3, 5, 8, 8, 9, 12, 13, 9, 9 (Mode is 9, as it appears three times)
• S₂: 7, 4, 7, 8, 7, 8, 13 (Mode is 7, as it appears three times)

Now let's combine S₁ and S₂ to form a new series:

• Combined Series: 3, 5, 8, 8, 9, 12, 13, 9, 9, 7, 4, 7, 8, 7, 8, 13

Now in the combined series, the mode is 7 as well as 9, because both numbers appear four times each. Therefore, combining S₁ and S₂ has changed the mode when compared to the mode of each series individually.