i need help with this Question
The following data represents Total Credit Hours from our class survey.
90 54 98 45 65 43 12 48 56 12 15 60 38 18 67 125 50 43 26 64 22 52 69
You may use your calculator to find the following statistics:
Mean __________ Median _______
Mode (if it exists) ___________
Give the Five Number Summary:
Min _________ Q1 _________ Med _________ Q3 _________ Max _________
Find the Interquartile Range (show your work) _____________________
Considering the Total Credit Hours data from our class survey:
(A1) What percent of the data should be less than Q3 on all box plots? ___________
(A2) What percent of this data is actually less than Q3 ? ___________
(B1) What percent of the data should be between Q1 and Q3 on all box plots? ___________
(B2) What percent of this data is actually between Q1 and Q3? ___________
If the percentages are not the same in (A) or (B) above, why is this happening?
Find the values for the fences (show your work). Are there any potential outliers? Yes or No
Lower fence ________________________
Upper fence ________________________
Potential Outliers (if they exist) ________________________
If there are potential outliers, what are the adjacent values? _____________________
i really need more help with A1, A2, B1, B2. the most
A1) 75%
A2) Should be the same.
B1) 50%
Not same, because below Q3 includes 25% below Q1.
To solve this question, we will need to perform several calculations and identify statistical measures. Let's go step by step:
Step 1: Calculate Mean and Median
To find the mean, add up all the data values and divide by the total number of values. For this data set, the calculation is as follows:
Mean = (90 + 54 + 98 + 45 + 65 + 43 + 12 + 48 + 56 + 12 + 15 + 60 + 38 + 18 + 67 + 125 + 50 + 43 + 26 + 64 + 22 + 52 + 69) / 23
Mean = 1037 / 23 = 45.09 (rounded to two decimal places)
To find the median, sort the data in increasing order and find the middle value. The median for this data set is 50.
Mean = 45.09, Median = 50
Step 2: Calculate Mode (if it exists)
The mode is the value(s) that occur most frequently in the data set. In this case, there is no mode because no value repeats more than once.
Mode = N/A (No mode exists)
Step 3: Find the Five-Number Summary
The five-number summary consists of the minimum, Q1 (first quartile), median, Q3 (third quartile), and maximum values.
To find the five-number summary, start by sorting the data in increasing order:
12 12 15 18 22 26 38 43 43 45 48 50 52 54 56 60 64 65 67 69 90 98 125
Min = 12
Q1 = 26
Med = 50
Q3 = 65
Max = 125
Min = 12, Q1 = 26, Med = 50, Q3 = 65, Max = 125
Step 4: Calculate Interquartile Range (IQR)
The interquartile range is the range between Q1 and Q3. To find the IQR, subtract Q1 from Q3.
IQR = Q3 - Q1 = 65 - 26 = 39
IQR = 39
Step 5: Percentage Calculation
(A1) What percent of the data should be less than Q3 on all box plots?
Since Q3 represents the 75th percentile, 75% of the data should be less than Q3.
(A1) Percent of data less than Q3 = 75%
(A2) What percent of this data is actually less than Q3?
To calculate the percentage of data less than Q3, count the number of data points that are less than Q3 and divide it by the total number of data points (23).
Count of data less than Q3 = 10
Percentage of data less than Q3 = (10 / 23) * 100 = 43.48% (rounded to two decimal places)
(A2) Percent of data less than Q3 = 43.48%
(B1) What percent of the data should be between Q1 and Q3 on all box plots?
Since Q1 represents the 25th percentile and Q3 represents the 75th percentile, the middle 50% of the data should be between Q1 and Q3.
(B1) Percent of data between Q1 and Q3 = 50%
(B2) What percent of this data is actually between Q1 and Q3?
To calculate the percentage of data between Q1 and Q3, count the number of data points that fall within this range (26 to 65) and divide it by the total number of data points (23).
Count of data between Q1 and Q3 = 8
Percentage of data between Q1 and Q3 = (8 / 23) * 100 = 34.78% (rounded to two decimal places)
(B2) Percent of data between Q1 and Q3 = 34.78%
If the percentages in (A) or (B) are not the same, the discrepancy occurs because the data set is small and discrete, causing the calculated percentages to differ from the expected theoretical percentages.
Step 6: Calculate the Fences and Identify Potential Outliers
To calculate the fences, multiply the IQR by 1.5 and add/subtract the result from Q1 and Q3, respectively.
Lower Fence = Q1 - (1.5 * IQR) = 26 - (1.5 * 39) = -28.5 (rounded to one decimal place)
Upper Fence = Q3 + (1.5 * IQR) = 65 + (1.5 * 39) = 121.5 (rounded to one decimal place)
Since the lower fence is negative, we can disregard it, as credit hours can't be negative. Therefore, there are no potential outliers based on the lower fence.
If any data point falls below the lower fence or above the upper fence, it is considered a potential outlier. In this case, there are no potential outliers.
Lower Fence = -28.5
Upper Fence = 121.5
Potential Outliers = None
Since there are no potential outliers, there are no adjacent values to consider.
I hope this explanation helps you understand how to solve the given question. If you have any further queries, feel free to ask!