select the correct answer from each drop - down menu. james needs to clock a minimum of 9 hours per day at…

select the correct answer from each drop - down menu. james needs to clock a minimum of 9 hours per day at work. the data set records his daily work hours, which vary between 9 hours and 12 hours, for a certain number of days. 9, 9.5, 10, 10.5, 10.5, 11, 11, 11.5, 11.5, 11.5, 12, 12 the median number of hours james worked is 11. the skew of the distribution is negative, positive, zero, zero with symmetry

select the correct answer from each drop - down menu. james needs to clock a minimum of 9 hours per day at work. the data set records his daily work hours, which vary between 9 hours and 12 hours, for a certain number of days. 9, 9.5, 10, 10.5, 10.5, 11, 11, 11.5, 11.5, 11.5, 12, 12 the median number of hours james worked is 11. the skew of the distribution is negative, positive, zero, zero with symmetry

Answer

Explanation:

Step1: Arrange data in order

The data set [9, 9.5, 10, 10.5, 10.5, 11, 11, 11.5, 11.5, 11.5, 12, 12] is already in ascending - order. There are (n = 12) data points.

Step2: Calculate the median

For a data - set with (n) data points (where (n) is even), the median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+1))th ordered values. Here, (\frac{n}{2}=6) and (\frac{n}{2}+1 = 7). The 6th value is 11 and the 7th value is 11, so the median (M=\frac{11 + 11}{2}=11).

Step3: Determine the skew

The mean of the data set (\bar{x}=\frac{9+9.5 + 10+10.5+10.5+11+11+11.5+11.5+11.5+12+12}{12}=\frac{129}{12}=10.75). Since the mean (10.75<) median (11), the distribution is negatively skewed.

Answer:

The median number of hours James worked is 11. The skew of the distribution is negative.