Example 1.
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16 8 9 4 0 Example 1. The number of goals scored by Premier League teams over a weekend was recorded in a table. Calculate the mean and the mode. Mean from a Frequency Table fx Frequency, f Goals x Calculating the Mean : If there are large amounts of data, it is easier if it is displayed in a frequency table. 0 1 2 3 4 5 2 4 8 3 2 1 5 ∑f= 20 ∑fx= 42 Mean = ∑fx ∑f = 42 20 = 2.1 Probably Middlesbrough and Sunderland Mode
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Mean from a Frequency Table. Calculating the Mean : If there are large amounts of data, it is easier if it is displayed in a frequency table. Example 1. The number of goals scored by Premier League teams over a weekend was recorded in a table. Calculate the mean and the mode. Goals x. - PowerPoint PPT Presentation
Transcript of Example 1.
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Example 1.The number of goals scored by Premier League teams over a weekend was recorded in a table. Calculate the mean and the mode.
Mean from a Frequency Table
fxFrequency, fGoals x
Calculating the Mean: If there are large amounts of data, it is easier if it is displayed in a frequency table.
0
1
2
3
4
5
2
4
8
3
2
1 5
∑f= 20 ∑fx= 42
Mean =∑fx
∑f
= 42
20
=
2.1
Probably Middlesbrough and Sunderland
Mode
Large quantities of data can be much more easily viewed and managed if placed in groups in a frequency table. Grouped data does not enable exact values for the mean, median and mode to be calculated. Alternate methods of analyising the data have to be employed.
Example 1.During 3 hours at Heathrow airport 55 aircraft arrived late. The number of minutes they were late is shown in the grouped frequency table below.
Grouped Data
250 - 60
440 - 50
530 - 40
720 - 30
1010 - 20
270 - 10
frequencyminutes lateData is grouped into 6 class intervals of width 10.
Example 1.During 3 hours at Heathrow airport 55 aircraft arrived late. The number of minutes they were late is shown in the grouped frequency table below.
Grouped Data
midpoint(x) fx
250 - 60
440 - 50
530 - 40
720 - 30
1010 - 20
270 - 10
Frequency,fminutes Late
Estimating the Mean: An estimate for the mean can be obtained by assuming that each of the raw data values takes the midpoint value of the interval in which it has been placed.
5
15
2535
45
55
135
150
175
175
180
110
Mean estimate = 925/55 = 16.8 minutes
55f 925f x
Example 1.During 3 hours at Heathrow airport 55 aircraft arrived late. The number of minutes they were late is shown in the grouped frequency table below.
Grouped Data
The Modal Class
250 - 60
440 - 50
530 - 40
720 - 30
1010 - 20
270 - 10
frequencyminutes late
The modal class is simply the class interval of highest frequency.
Modal class = 0 - 10
(55+1)/2= 28
Example 1.During 3 hours at Heathrow airport 55 aircraft arrived late. The number of minutes they were late is shown in the grouped frequency table below.
Grouped Data
The Median Class Interval
The Median Class Interval is the class interval containing the median.
250 - 60
440 - 50
530 - 40
720 - 30
1010 - 20
270 - 10
frequencyminutes late
The 28th data value is in the 10 - 20 class
Data is grouped into 8 class intervals of width 4.
Example 2.A group of University students took part in a sponsored race. The number of laps completed is given in the table below. Use the information to: (a) Calculate an estimate for the mean number of laps.(b) Determine the modal class.(c) Determine the class interval containing the median.
Grouped Data
136 - 40
231 – 35
2526 – 30
1721 – 25
2016 – 20
1511 – 15
96 – 10
21 - 5
frequency (x)number of laps
mp x fmidpoint(x)
136 - 40
231 – 35
2526 – 30
1721 – 25
2016 – 20
1511 – 15
96 – 10
21 - 5
frequencynumber of laps
Example 2.A group of University students took part in a sponsored race. The number of laps completed is given in the table below. Use the information to: (a) Calculate an estimate for the mean number of laps.(b) Determine the modal class.(c) Determine the class interval containing the median.
Grouped Data
3
8
1318
23
2833
38
6
72195360
39170066
381828fx 91f
Mean estimate = 1828/91 = 20.1 laps
Modal Class 26 - 30
Grouped Data
Example 2.A group of University students took part in a sponsored race. The number of laps completed is given in the table below. Use the information to: (a) Calculate an estimate for the mean number of laps.(b) Determine the modal class. (c) Determine the class interval containing the median.
136 - 40
231 – 35
2526 – 30
1721 – 25
2016 – 20
1511 – 15
96 – 10
21 - 5
frequency (x)number of laps
136 - 40
231 – 35
2526 – 30
1721 – 25
2016 – 20
1511 – 15
96 – 10
21 - 5
frequency (x)number of laps
Example 2.A group of University students took part in a sponsored race. The number of laps completed is given in the table below. Use the information to: (a) Calculate an estimate for the mean number of laps.(b) Determine the modal class. (c) Determine the class interval containing the median.
Grouped Data
(91+1)/2 = 46
91f
The 46th data value is in the 16 – 20 class
Weighted Means
• Grade point average (GPA): Most colleges assign "weights" to the individual course grades in the form of credits. A grade in a 4-credit course affects your GPA more than a grade in a 3-credit course. For example, suppose Joe took the following courses:
• COURSE CR GR
Calculus 4 C
Discr. Math 3 A
English Lit. 3 A
Chemistry 4 D
Comp. Sci. 3 B
• Most colleges use the scale: A = 4, B = 3, C = 2, D = 1, F = 0. To compute Joe's GPA, we multiply each course grade (converted to the number equivalent) by the course credits, then divide the sum by the total number of credits:
COURSE CR GR
Calculus 4 C 4*2 = 8
Discr. Math 3 A 3*4 = 12
English Lit. 3 A 3*4 = 12
Chemistry 4 D 4*1 = 4
Comp. Sci. 3 B 3*3 = 9
---- ----
17 45
GPA = 45 / 17 = 2.65
• Example:Grades are often computed using a weighted average. Suppose that homework counts 10%, quizzes 20%, and tests 70%.If Pat has a homework grade of 92, a quiz grade of 68, and a test grade of 81, then find Pat’s overall grade
Pat's overall grade = (0.10)(92) + (0.20)(68) + (0.70)(81)
= 79.5
Homework
• Pg. 117, 118 #12-15, 26-30
For 12-15 find mean, modal class, and median interval
