Question

Which of the following statements is true based on the data set shown below?

A) Median = mode

B) Mode = mean

C) Mean = median

Answer 1

The answer is the first choice, "Median=Mode."

The median (middle number of a data set) is 15, and the mode (number that appears most frequently) is also 15.

Answer 2

We have:

Median=Mode

Explanation:

We are given data as:

Speed(x) Frequency(y) Cumulative Frequency

12 1

13 2 1+2=3

14 6 3+6=9

15 12 9+12=21

16 6 21+6=27

17 5 27+5=32

18 1 32+1=33

19 2 33+2=35

20 4 35+4=39

21 1 N= 39+1=40

N=40

As the total number of frequency is even i.e. 40.

`(N+1)/(2)=20.5`

Hence, the median lie between the 20 and 21.

Hence,Median=15

We know that the mode is the data corresponding to highest frequency.

Hence here Mode=15 ( Since it's frequency is highest i.e. 12)

Also, Mean is calculated by:

x y xy

12 1 12

13 2 26

14 6 84

15 12 180

16 6 96

17 5 85

18 1 18

19 2 38

20 4 80

21 1 21

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∑xy=640

Hence, Mean is calculated as:

`Mean=(\sum xy)/(N)\\\\\\Mean=(640)/(40)\\\\Mean=16`

Hence, Mean=16

Hence, we have:

Median=Mode=15