8.2 The following data represents the ages of 21 students in a class: 22, 24, 19
ID: 3224978 • Letter: 8
Question
8.2 The following data represents the ages of 21 students in a class: 22, 24, 19, 17, 20, 27, 24, 23, 26, 17, 19, 22, 25, 21, 21, 22, 22, 21, 21, 20, 22. a. What is the mean of the data set? b. What is the median? c. What is the mode? 8.3 The scores in a class quiz are as follows: 58, 62, 62, 63, 65, 65, 65, 68, 69, 72, 72, 75, 76, 78, 79, 81, 84, 84, 85, 92, 94, 95, 98. a. What is the mean score in the quiz? b. What is the median score in the quiz? c. What is the mode of the quiz? Section 8.4 Measures of Dispersion 8.4 Consider the following set of data: 15, 20, 21, 20, 36, 15, 25, 15. d. What is the variance? e. What is the interquartile range? 8.5 The following data represents the ages of 21 students in a class: 22, 24, 19, 17, 20, 27, 24, 23, 26, 17, 19, 22, 25, 21, 21, 22, 22, 21, 21, 20, 22. a. What is the variance? b. What is the range? c. What is the interquartile range?Explanation / Answer
SOlutiuon8.2
The mean value of the data set is:
21.6667
Explanation
The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:
Mean=Sum of terms/Number of terms
=455/21
=21.667
Median:
The median of the data set is 22.
Explanation
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
17 17 19 19 20 20 21 21 21 21 22 22 22 22 22 23 24 24 25 26 27
So, the median is 22 .
Mode:
The mode of the data set is 22.
Explanation
The mode of a set of data is the value in the set that occurs most often.
Ordering the data from least to greatest, we get:
17 17 19 19 20 20 21 21 21 21 22 22 22 22 22 23 24 24 25 26 27
We see that the mode is 22 .
22 repeats 5 times
so mde 22
Solution8.5:
Inter quartile range=q3-q1
The third quartile of the data set is 23.5.
Explanation
The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.
17 17 19 19 20 20 21 21 21 21 22 22 22 22 22 23 24 24 25 26 27
So, the upper half is
22 22 22 22 23 24 24 25 26 27
The median of these numbers is 23.
so Q3=23
The first quartile of the data set is 20.
Explanation
The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.
17 17 19 19 20 20 21 21 21 21 22 22 22 22 22 23 24 24 25 26 27
So, the bottom half is
17 17 19 19 20 20 21 21 21 21
The median of these numbers is 20.
Q1=20
The interquartile range of the data set is 3.5.
Explanation
The interquartile range is the difference between the third and first quartiles.
The third quartile is 23.5.
The first quartile is 20.
The interquartile range = 23.5 - 20 = 3.5.
he variance of the data set is:
var=6.8333
Explanation
To find variance we use the following formula
var=(xiX¯¯¯)2n1
We will compute this formula in 4 steps.
Step 1: Find the mean. (X¯¯¯)
HERE : X¯¯¯=21.6667
Step 2: Create the following table.
Step 3: Find the sum of numbers in the last column to get.
(xiX¯¯¯)2=136.6667
Step 4: Calculate variance using the above formula.
var=(xiX¯¯¯)2/n1=136.6667/2116.8333
REST OF THE QUESTIONS POST SEPERATELY
data data-mean (data - mean)2 22 0.3333 0.11108889 24 2.3333 5.44428889 19 -2.6667 7.11128889 17 -4.6667 21.77808889 20 -1.6667 2.77788889 27 5.3333 28.44408889 24 2.3333 5.44428889 23 1.3333 1.77768889 26 4.3333 18.77748889 17 -4.6667 21.77808889 19 -2.6667 7.11128889 22 0.3333 0.11108889 25 3.3333 11.11088889 21 -0.6667 0.44448889 21 -0.6667 0.44448889 22 0.3333 0.11108889 22 0.3333 0.11108889 21 -0.6667 0.44448889 21 -0.6667 0.44448889 20 -1.6667 2.77788889 22 0.3333 0.11108889Related Questions
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