Question

Skew of Distribution

Answer 1

For the answer to the question above asking what the data set is, if the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference of the mean and the median?
For the 1st data set: 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8

mean: 3.5
median: 3

2nd Data set: 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 7, 8

mean: 3.78
median: 3.5

difference in mean: 3.78 - 3.5 = 0.28
difference in median: 3.5 - 3 = 0.50

Answer 2

Answer:  The skew in the distribution is positive. If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference of the mean and the median for the new data set is 0.28.

Step-by-step explanation:

Given data : {1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8}

$\text{Mean }=\dfrac{\text{Sum of all data values}}{\text{Number of data values}}\\\\\Rightarrow\ \text{Mean }=\dfrac{56}{16}=3.5$

Now, data is already arranged in ascending order.

Since number of observations (16) is even.

Median = Mean of $(\dfrac{16}{2}\text{ and } \dfrac{16}{2}+1)^{th}\text{term}$

=Mean of $(8^{th}\text{ and }9^{th} \text{term})$

⇒Median$=\dfrac{3+3}{2}=3$

Since, Median < Mean

Then , the data is positively skewed.

The new data set :  {1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8,5,7}

Number of data values :18

Now, $\text{Mean }=\dfrac{68}{18}=3.77777\approx3.8$

Again number of observations (18) is even.

Median = Mean of $(\dfrac{18}{2}\text{ and } \dfrac{18}{2}+1)^{th}\text{term}$

=Mean of $(9^{th}\text{ and }10^{th} \text{term})$

⇒Median$=\dfrac{3+4}{2}=3.5$

Difference of the mean and the median for the new data set is $3.78-3.5=0.28$