Question

For the given data  -1, 0, 1, 2, 3, 5, 5, 6, 8, 10, 11

which one of the following is true?

1. Mean = Median = Mode
2. Mean = Mode
3. Median = Mode
4. None of the above

Answer 1

Correct Answer - Option 3 : Median = Mode

Concept

1) Mean is the arithmetic average of a data set. This is found by adding the numbers in a data set and dividing by the number of observations in the data set.

2) The median is the middle number in a data set when the numbers are listed in either ascending or descending order.

If total number of observation (n) is odd then, Median = (n + 1)^th/2 observation

If total number of observation (n) is even then, Median = [(n/2)^th + {(n/2) + 1}^th]/2

3) The mode is the value that occurs the most often in a data set.

Calculation

There are 11 terms in the data

Data is -1, 0, 1, 2, 3, 5, 5, 6, 8, 10, 11

Mean = (-1 + 0 + 1 + 2 + 3 + 5 + 5 + 6 + 8 + 10 + 11)/11

⇒ 50/11

Median = (n + 1)th/2 observation

⇒ (11 + 1)/2 = 6^th term = 5

Mode = 5 [as 5 is repeated twice and all other terms are single]

So, we get Mean = 50/11, Median = 5, Mode = 5

∴ Median = Mode