grade 12 data management questions

Question

1. A survey asked randomly chosen Star Wars fans how many times they watched any of the 6 movies in the series in the past six months. When the position of the percentile falls in a range, pick the midpoint of that range.

Times Watched	Frequency
0 – 2	2
3 – 5	5
6 – 8	17
9 – 11	24
12 – 14	21
15 – 17	9
18 – 20	1

a)      Find the median, first quartile, and third quartile for the data.                                                   

Q₁ =                                                              Q₂ = median =                                                   Q₃ =

b)     Calculate the mean and the mode for the data.                                                                                 

Answer 1

Hi Pankhudi,

One option is to use a graphing calculator and input the values for the times watched (can't put intervals, so you can choose a value in the interval) and frequency into L1 and L2 and use the 1-Var Stats function (by going to STAT --> CALC --> 1-Var Stats.) You'll be shown List and FreqList so make sure you input L1 and L2 accordingly. Using this function will give you first quartile, median, third quartile, mean, and mode.

Another option is to add up the frequencies and cut it in half to find the middle. So when we divide 79/2 we get 39.5. In order to figure out where this lies in the table, count up or down from the first frequency (i.e. if you start at the top add 2+5+17+... until you get to either at or above 39.5).

So if we start at the top, we get down to the interval 9-11 so 10 will be our median.

I would suggest for the quartiles and mean to use the calculator instead of having to write out all of the numbers to find the medians of the two half sets separated by the median (which is what the first and third quartiles would be).

The first quartile is 7.

The third quartile is 11.

The mode is the number that occurs the most thus it would be 10.

The mean is the average which would be approximately 9.81.