Question

Question 16
Which of the following has the same mean, median and mode?
(a) 6, 2, 5, 4, 3, 4, 1
(b) 4, 2, 2, 1, 3, 2, 3
(c) 2, 3, 7, 3, 8, 3, 2
(d) 4, 3, 4, 3, 4, 6, 4

Answer 1

We have to find out the measure of central tendencies in the four given data.
For option (a)
Data (in ascending order) $\to$ 1, 2, 3, 4, 4, 5, 6
Here, n = 7 (odd)
Median =Value of $\left(\frac{n+1}{2}\right)$th observation = Value of $\left(\frac{8}{2}\right)$th observation = 4
Mean $=\frac{Sumofobservations}{n}=\frac{1+2+3+4+4+5+6}{7}=\frac{25}{7}=3.57$
Mode = Most frequent observation = 4
Hence,
Mean $\ne$ Median = Mode
For option (b)
Data (in ascending order) $\to$ 1, 2, 2, 2, 3, 3, 4
Here, n = 7 (odd)
Median =Value of $\left(\frac{n+1}{2}\right)$th observation = Value of $\left(\frac{8}{2}\right)$th observation = 2
Mean $=\frac{Sumofobservations}{n}=\frac{1+2+2+2+3+3+4}{7}=\frac{25}{7}=2.428$
Mode = Most frequent observation = 2
Hence,
Mean $\ne$ Median = Mode
For option (c)
Data (in ascending order) $\to$ 2, 2, 3, 3, 3, 7, 8
Here, n = 7 (odd)
Median = Value of $\left(\frac{n+1}{2}\right)$th observation = Value of $\left(\frac{7+1}{2}\right)$th observation = 3
Mode = Most frequent data = 3
$Mean=\frac{Sumofobservations}{n}=\frac{2+2+3+3+3+7+8}{7}=\frac{28}{7}=4$
Hence,
Mean $\ne$ Median = Mode
For option (d)
Data (in ascending order) $\to$ 3, 3, 4, 4, 4, 4, 6
Here, n = 7 (odd)
Median = Value of $\left(\frac{n+1}{2}\right)$ th observation = Value of $\left(\frac{7+1}{2}\right)$th observation = 4
Mode = Most frequent data = 4
$Mean=\frac{Sumofobservations}{n}=\frac{3+3+4+4+4+4+6}{7}=\frac{28}{7}=4$
Hence,
Mean = Mode = Median