Identify any outliers in the following data set by first calculating the median and the interquartile range.
Number of texts sent Frequency Cumulative Frequency
0 10 10
1 8 18
0 5 23
0 3 26
0 1 27
Median I got was 14 (27/2 = 13.5 rounded up to 14) = score 1, please correct me if this is the incorrect way of finding the median.
For q1 and q2 answers say:
Q1 = 7th score = 0
Q3 = 21st score = 2
How the heck do I calculate Q1 and Q3 from the table without typing in each number one by one... Just need clarification on this, the rest I should be able to do, thanks.
Sorry, the table got messed up, but the first column lines up with "number of texts sent", second column, with frequency and last column with cumulative frequency.
Nvm Q1 is just 1/4 of the cumulative freq. and Q3 is 3/4 of the cumulative freq...
To calculate the first quartile (Q1) and the third quartile (Q3) from the given data set, you can use the cumulative frequency values.
Firstly, find the cumulative frequency value that corresponds to Q1. Q1 represents the 25th percentile, so you need to find the cumulative frequency that is closest to or greater than 25% of the total cumulative frequency.
In this case, the total cumulative frequency is 27. Looking at the cumulative frequency column, you can see that the cumulative frequency value of 23 is the closest value to or greater than 25%. This means that the first quartile (Q1) is at the value of 0, as indicated in your table.
Now, for Q3, you need to find the cumulative frequency value that corresponds to the 75th percentile. Again, looking at the cumulative frequency column, you can see that the cumulative frequency value of 27 represents the total data set. Therefore, Q3 is at the value of 2, as also indicated in your table.
To summarize:
Q1 = 0
Q3 = 2
I hope this clarifies the calculation of Q1 and Q3 from the given data set. Let me know if you have any further questions.
To calculate the first quartile (Q1) and the third quartile (Q3) from the given table, you can use the cumulative frequency.
1. Find the total number of data points in the set. In this case, the cumulative frequency is 27, so there are 27 data points.
2. Calculate the position of Q1. The first quartile (Q1) is the value that is 25% of the way through the cumulative frequencies. In this case, 25% of 27 is 6.75, which rounds up to 7. Therefore, Q1 is the 7th score in the dataset, which is 0.
3. Calculate the position of Q3. The third quartile (Q3) is the value that is 75% of the way through the cumulative frequencies. In this case, 75% of 27 is 20.25, which rounds up to 21. Therefore, Q3 is the 21st score in the dataset, which is 2.
Now that you have Q1 = 0 and Q3 = 2, you can calculate the interquartile range (IQR) by subtracting Q1 from Q3: IQR = Q3 - Q1 = 2 - 0 = 2.
To identify outliers, you can consider any data point that is below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. In this case, there are no outliers since all the scores are either 0 or 1, and within the range.
Regarding your calculation of the median, you are correct. To find the median, you need to divide the total cumulative frequency by 2 and then identify the corresponding score. In this case, 27 divided by 2 is 13.5, which rounds up to 14. Therefore, the median is the 14th score in the dataset, which is 1.