The following data set gives the difference between the winning and?

losing scores in 50 randomly observed high school basketball games: 2, 12, 1, 2, 12, 5, 14, 2, 45, 9, 1, 8, 18, 28, 9, 4, 30, 16, 4, 12, 8, 13, 20, 9, 17, 13, 49, 17, 13, 4, 14, 2, 12, 29, 8, 9, 11, 4, 6, 22, 4, 20, 23, 9, 14, 11, 8, 8, 2, 8.
A) Make a frequency table detailing the occurrence of each score difference.
B) Find the relative frequency of each score difference observed.
C) Make a stem-and-leaf plot of the data from this experiment.
D) Develop appropriate intervals and make a histogram for this data

I've made the frequency table if someone can just check it and then I don't know where to go from there?

a) Frequency table:
( value, frequency)
(1,2)
(2,5)
(4,5)
(5,1)
(6,1)
(8,6)
(9,5)
(11,2)
(12,4)
(13,3)
(14,3)
(16,1)
(17,2)
(18,1)
(20,2)
(22,1)
(23,1)
(28,1)
(29,1)
(30,1)
(45,1)
(49,1)

Okay and I have done C. I need help with B and D.

C) Stem-and-leaf is just listing the numbers in sorted order, with the tens on one side of a dividing line, and the ones (last digits) on the other. You write all the individual last ones on the same line:

0 | 1 1 2 2 2 2 2 4 4 4 4 4 5 6 8 8 8 8 8 8 9 9 9 9 9
1 | 1 1 2 2 2 2 3 3 3 4 4 4 6 7 7 8
2 | 0 0 2 3 8 9
3 | 0
4 | 5 9

Thanks!

Your frequency table looks correct so far. Now let's move on to the next steps.

b) To find the relative frequency of each score difference observed, you need to divide the frequency of each score difference by the total number of observations. In this case, the total number of observations is 50.

To calculate the relative frequency, divide each frequency by 50. For example, for a score difference of 1, the frequency is 2, so the relative frequency would be 2/50 = 0.04.

You can calculate the relative frequency for each score difference in your frequency table accordingly.

c) A stem-and-leaf plot is a way to visualize the data. To create a stem-and-leaf plot, separate each score difference into a stem and leaf. The stem represents the tens digit and the leaf represents the ones digit.

For example, the score difference 12 would be separated as 1 (stem) and 2 (leaf).

Using your frequency table, create the stem-and-leaf plot by grouping the score differences based on their tens digit.

Here's an example:

1 | 2 2
2 | 1
4 | 4 4 4 4
5 | 1
6 | 6
8 | 8 8 8 8 8 8
9 | 9 9 9 9 9
1 | 1 1
...

d) To create a histogram, you need to group the score differences into intervals. Here, we can create intervals of 10, starting from 0 to 50. So the intervals would be:
0-9, 10-19, 20-29, 30-39, 40-49.

Count the number of score differences that fall within each interval and plot the counts using bars on the x-axis.

Your histogram would look something like this:

|
8 |
|
7 |
|
6 |
| 4
5 | |
| |
4 | | 4
| | |
3 | | |
| | |
2 | | | 3
| | | |
1 | | | |
| | | |
______________
0 10 20 30 40 50

Note: The numbers on the y-axis represent the frequencies or counts of score differences that fall within each interval.

I hope this helps! Let me know if you have any more questions.

Great job on creating the frequency table! Now let's move on to the next steps:

B) To find the relative frequency of each score difference observed, you need to divide the frequency of each score difference by the total number of observations (which in this case is 50). This will give you the proportion or probability of each score difference occurring. For example:

Relative frequency of 1 = Frequency of 1 / Total number of observations = 2/50 = 0.04
Relative frequency of 2 = Frequency of 2 / Total number of observations = 5/50 = 0.1
...

You can compute the relative frequency for each score difference in a similar manner. Remember to round your answers to an appropriate decimal place.

C) A stem-and-leaf plot is a way to represent data graphically. It splits each data point into a "stem" and a "leaf", using the stems to group similar data points. To create a stem-and-leaf plot for this data, follow these steps:

1. Separate the two-digit score differences into stems and leaves. The stem represents the tens digit, and the leaf represents the ones digit.
2. Arrange the stems in ascending order and write them down vertically.
3. For each stem, list the corresponding leaves next to it.
4. Include a key to indicate the units (leaves) corresponding to each stem.

For example, if you have the score differences 12, 13, and 14, the stem would be "1" and the leaves would be "2", "3", and "4" respectively.

D) To create an appropriate histogram for this data, follow these steps:

1. Decide on the number of intervals (bins) you want to use. This will depend on the range of the data and how you want to group it. For example, you could choose intervals of size 5, 10, or any other value that makes sense given the data.
2. Determine the range of the score differences. In this case, the minimum score difference is 1 and the maximum is 49, so the range is 49 - 1 = 48.
3. Divide the range by the number of intervals to determine the interval width. For example, if you choose 5 intervals, the interval width would be 48 / 5 = 9.6. Round this up to the nearest whole number to determine the width of each interval.
4. Starting from the minimum score difference, create intervals of the determined width. Count the number of score differences that fall within each interval and create bars in the histogram to represent these intervals.

I hope this helps! Let me know if you have any further questions.