Question

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

Explanation:

Step1: Count data - points

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

Step2: Find the median

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

Step3: Calculate the mean

\(\bar{x}=\frac{5\times1 + 6\times1+7\times1 + 8\times1+9\times3+10\times4+11\times2+12\times1}{14}=\frac{5 + 6+7 + 8+27+40+22+12}{14}=\frac{127}{14}\approx9.07\)

Step4: Analyze the distribution shape

The distribution is slightly right - skewed. In a right - skewed distribution, the mean is pulled in the direction of the tail (the larger values), so the mean is greater than the median.

Answer:

The mean is greater. The mean is approximately 9.07 and the median is 9. The distribution is right - skewed, which causes the mean to be pulled towards the larger values, making it greater than the median.