Question

If the mode of the data 5, 3, 4, -2, 3, 2, 2, 1, p is 3, then the value of p is:
a.) 2
b.) 5
c.) -2
d.) 3

Answer 1

Hint: We will use the definition of mode. At first, we will arrange the given data in ascending order or in descending order and then count how many of each number, and the number which occurs maximum number of times is the mode of the given data.

Complete step by step answer:
First, we will define the mode. Mode of the given data is the number which occurs the maximum number of times in the given data.
To find the mode of the given data we will first arrange in order the given data and then find the number which occurs the maximum number of times. The number which occurs the maximum number of times in the given data is mode of the given data.
So, we will arrange the given data (i.e. 5, 3, 4, -2, 3, 2, 2, 1, p) in ascending order.
Since, we do not know the value of p so we will first arrange the given data into ascending order except p.
So, after arranging the given data into ascending we can write the data as: -2, 1, 2, 2, 3, 3, 4, 5, p.
From the data we can see that 2 and 3 both occur 2 times but the mode of data which is given in question is 3.
So, 3 must occur the maximum number of times in the given data.
Since, both 2 and 3 occur an equal number of times so for the mode to be equal to 3, p must be equal to 3 and hence occurrence of 3 will then become maximum and hence mode is equal to 3.

So, the correct answer is “Option D”.

Note: Most of the students calculate the value of mode directly without arranging the given data but there are so many chances of making mistakes so students are requested to avoid that method and follow the method as stated above.