Question

the number of writing instruments in some teachers desks is displayed in the dot plot. number of writing instruments which is greater, the mean or the median? the mean the median explain your reasoning, using the shape of the distribution

Explanation:

Step1: Count the number of data - points

There are 1 + 1+ 1+ 1+ 3+ 4+ 2+ 1 = 14 data - points.

Step2: Find the median

Since \(n = 14\) (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered data - points. The 7th and 8th ordered data - points are both 9, so the median \(M=\frac{9 + 9}{2}=9\).

Step3: Calculate the mean

The sum of the data is \(5\times1+6\times1 + 7\times1+8\times1+9\times3+10\times4+11\times2+12\times1\)
\[=5 + 6+7+8+27+40+22+12\]
\[=(5 + 6+7+8)+(27+40)+(22+12)\]
\[=26+67+34\]
\[=127\]
The mean \(\bar{x}=\frac{127}{14}\approx9.07\)

Answer:

the mean