The following data represents the GPA of a sample of 15 students enrolled in a math class. Use technology and round to 4 decimal places. GPA2.63.083.473.311.832.812.243.993.322.541.822.822.822.72.01(a) Find the first quartile. (b) Find the third quartile. (c) Find the mean. (d) Find the median. (e) Find the range. (f) Find s. (g) Find the interquartile range. (h) What are the lower and upper limits to find outliers? LL: UL:(i) Find s2.
Question
The following data represents the GPA of a sample of 15 students enrolled in a math class. Use technology and round to 4 decimal places. GPA2.63.083.473.311.832.812.243.993.322.541.822.822.822.72.01(a) Find the first quartile. (b) Find the third quartile. (c) Find the mean. (d) Find the median. (e) Find the range. (f) Find s. (g) Find the interquartile range. (h) What are the lower and upper limits to find outliers? LL: UL:(i) Find s2.
Solution
(a) First Quartile (Q1): To find the first quartile, we first need to sort the data in ascending order. Then, Q1 is the median of the first half of the data.
(b) Third Quartile (Q3): Similarly, Q3 is the median of the second half of the data.
(c) Mean: The mean is the sum of all the data points divided by the number of data points.
(d) Median: The median is the middle value when the data is sorted in ascending order. If there is an even number of data points, the median is the average of the two middle values.
(e) Range: The range is the difference between the highest and lowest data points.
(f) s (Standard Deviation): The standard deviation is a measure of how spread out the numbers are from the mean. It is calculated by taking the square root of the variance.
(g) Interquartile Range (IQR): The IQR is the range of the middle 50% of the data, calculated as Q3 - Q1.
(h) Lower Limit (LL) and Upper Limit (UL) for Outliers: The LL is calculated as Q1 - 1.5IQR and the UL is calculated as Q3 + 1.5IQR. Any data points outside these limits are considered outliers.
(i) s^2 (Variance): The variance is the average of the squared differences from the mean. It is calculated by squaring the standard deviation.
Please note that the actual calculations would require the specific GPA values and a calculator or statistical software.
Similar Questions
For the following set of data, what is the interquartile range?x = { 6, 8, 9, 12, 14, 15, 17 }Exclude the median in any calculations requiring quartiles.1 point761598
In the data set below, what are the lower quartile, the median, and the upper quartile?2345577779lower quartile = median = upper quartile =
Finally, find Q3.Recall that the third quartile, Q3, is the median of the upper half of the data. That is, the median of the data located above the Q2 position.Consider the ordered list of data values. The median, Q2, which has been determined, has been underlined for clarity.3, 6, 6, 7, 8, 8, 9, 10, 11There are nine values in the whole data set, but there are only values to the right of the underlined median. The third quartile, Q3, will be equal to the median of these values.Since the lower half of the data has an even number of data values, we will now use the rule to find the median of an even number of data values.median = sum of middle two values2The middle two values of the upper half are 9 and .Now, calculate the third quartile, Q3.Q3 = 9 + 2 = 2 =
What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16?(a) 17 (b) 16 (c) 12.75 (d) 12
What is the third quartile of this data set?14, 18, 20, 21, 25, 32, 40, 44, 48A.44B.36C.42D.40
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.