Question

In: Statistics and Probability

Question 5: (Marks: 5) A group of students compared the number of times they have been...

Question 5: (Marks: 5)

A group of students compared the number of times they have been to the movies in the past year. The following table illustrates how many times each person went to the movie theatre in each month. You need to show your work.

Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sep.

Oct.

Nov.

Dec.

Eric

1

2

3

5

2

1

3

1

2

1

3

1

Kyle

1

2

1

3

1

2

3

2

2

1

4

2

Stan

1

3

2

2

2

1

5

3

2

2

3

3

Kenny

1

2

1

1

2

2

3

2

3

2

3

2
  1. By comparing modes, which person went to the movies the least per month?
  1. By comparing medians, which person went to the movies the most per month?
  1. Rank the students in order of most movies seen to least movies seen by comparing their means.

  1. Which month, by comparing the means of movies seen in each month, is the most popular movie-watching month?

  1. By comparing medians, which month is the least popular month?

Solutions

Expert Solution

Mode: The most frequent number—that is, the number that occurs the highest number of times.

Mode calculation:

Eric 1(5 times), 2(3 times), 3(3 times), 5(1 time) 1
Kyle 1(4 times), 2(5 times), 3(2 times), 4(1 time) 1
Stan 1(2 times), 2(5 times), 3(4 times), 5(1 time) 2
Kenny 1(3 times), 2(6 times), 3(3 times) 2

Q. By comparing modes, which person went to the movies the least per month?

ans: Eric and Kyle went to the moves least per month

Median: The middle number which one is found by ordering all data points and picking out the one in the middle (or if there are two middle numbers, taking the average of those two numbers).

Median calculation:

Eric 1(5 times), 2(3 times), 3(3 times), 5(1 time) (2+3)/2 = 2.5
Kyle 1(4 times), 2(5 times), 3(2 times), 4(1 time) (2+3)/2 = 2.5
Stan 1(2 times), 2(5 times), 3(4 times), 5(1 time) (2+3)/2 = 2.5
Kenny 1(3 times), 2(6 times), 3(3 times) 2

Q. By comparing medians, which person went to the movies the most per month?

ans: Comparing medians Eric, Kyle and Stan went to the movies the most per month

Mean: The average number, summing over all data points and dividing by the number of number of data points.

Mean calculation:

Jan Feb Mar April May June July Aug Sept Oct Nov Dec
mean (1+1+1+1)/4 = 1 (2+2+3+2)/4 = 2.25 (3+1+2+1)/4 = 1.75 (5+3+2+1)/4 = 2.75 (2+1+2+2)/4 = 1.75 (1+2+1+2)/4 = 1.5 (3+3+5+3)/4 = 3.5 (1+2+3+2)/4 = 2 9/4 = 2.25 6/4 = 1.5 13/4 = 3.25 8/4 = 2

Q. Which month, by comparing the means of movies seen in each month, is the most popular movie-watching month?

ans: By comparing the means of movies seen in each month, the most popular movie-watching month is July

Median table for months:

Jan Feb Mar April May June July Aug Sept Oct Nov Dec
median 1 2 1.5 2.5 2 1.5 3 2 2 1.5 3 2

Q. By comparing medians, which month is the least popular month?

ans: January is least popular month by comparing median.

orchestra answered 1 year ago
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