1 / 14

Example 1. The number of goals scored by a team in 20 games are given below :

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 a team in 20 games are given below :

amelia
Download Presentation

Example 1. The number of goals scored by a team in 20 games are given below :

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 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 a team in 20 games are given below : 3 , 2 , 4 , 2 , 2 , 3 , 2 , 2 , 0 , 5 , 1 , 1 , 2 , 3 , 0 , 2 , 1 , 4 , 1 , 0 Goals x Frequency, f f.x 0 3 1 4 Mean = ∑fx 7 2 3 ∑f 3 = 40 4 2 20 5 1 Mode 0 4 14 9 = 2 8 5 ∑f= 20 ∑fx= 40

  2. Median from a Frequency Table Calculating the median 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 a team in 20 games are given below : 3 , 2 , 4 , 2 , 2 , 3 , 2 , 2 , 0 , 5 , 1 , 1 , 2 , 3 , 0 , 2 , 1 , 4 , 1 , 0 Goals x Frequency, f C. F. 0 3 1 4 7 2 3 3 4 2 5 1 Mode (20)/2 = 10 3 (20)/2 + 1 = 11 7 14 17 The 10th value is 2 19 The 11th value is 2 20 ∑f= 20 ∴ MEDIAN = ( 2+2 ) / 2 = 4/2 = 2

  3. Grouped Data Large quantities of data can be much more easily viewed and managed if placedingroupsin afrequency 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. minutes late frequency 0 - 9 27 10 - 19 10 20 - 29 7 30 - 39 5 40 - 49 4 50 - 59 2 Data is grouped into 6 class intervals of width 10.

  4. Grouped Data 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. 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. minutes Late Frequency,f midpoint(c.c.) F × c.c. 0 - 9 27 10 - 19 10 20 - 29 7 30 - 39 5 40 - 49 4 50 - 59 2 4.5 121.5 145 14.5 171.5 24.5 34.5 172.5 44.5 178 54.5 109 Mean estimate = 897.5/55 ≈ 16.32 minutes

  5. Grouped Data The Modal Class The modal class is simply the class interval of highest frequency. 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. Modal class = 0 - 9 minutes late frequency 0 - 9 27 10 - 19 10 20 - 29 7 30 - 39 5 40 - 49 4 50 - 59 2

  6. worksheet For the following set of data find : بالنسبة لمجموعة البيانات التالية أوجد : 6 , 8 , 5 , 11 , 3 , 1 , 7 , 9 , 3 1) The mean 1) المتوسط الحسابي 1) The mean 1) المتوسط الحسابي 2) The median 2) الوسيط 2) The median 2) الوسيط 3) The mode 3) المنوال 3) The mode 3) المنوال 4) The range 4) المدى 4) The range 4) المدى For the following set of data find : بالنسبة لمجموعة البيانات التالية أوجد : 9 , 3 , 8 , 7 , 1 , 9 , 11 , 4 , 3 , 2

  7. worksheet The ages of a random sample of 30 persons are given in the table : أعمار عينة عشوائية من 30 شخص كما بالجدول : أوجد : Find : 1) The mean age 1) المتوسط الحسابي للأعمار 2) الوسيط للأعمار 2) The median 3) The mode 3) المنوال 4) The range of the ages 4) مدى الأعمار

  8. worksheet The following frequency distribution represents the lengths of 20 persons التوزيع التكراري يمثل أطوال 20 شخص أوجد : Find : 1) The mean of the lengths 1) المتوسط الحسابي للأطوال 2) The model class and estimate the mode 2) اكتب الفئة المنوالية وقدر المنوال 3) The range of the lengths 3) أوجد مدى الأطوال

  9. worksheet The grades of 25 students are given below : درجات 25 طالب كما يلي : 42 , 63 , 47 , 77 , 46 , 71 , 68 , 83 , 91 , 55 , 67 , 66 , 63 , 57 , 50 , 69 , 73 , 82, 77 , 58 , 66 , 79 , 88 , 97 , 86 1) Put the grades in a frequency table with intervals 1) ضع الدرجات في جدول تكراري ذو فئات 2) Draw the cumulative frequency polygon 2) ارسم المضلع التكراري التراكمي 3) Use the graph to estimate the median 3) استخدم الرسم لتقدر قيمة الوسيط

  10. Grouped Data The Median Class Interval The Median Class Interval is the class interval containing the median. 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. minutes late frequency 0 - 9 27 10 - 19 10 20 - 29 7 30 - 39 5 40 - 49 4 50 - 59 2 The 28th data value is in the 10 - 19 class (55+1)/2 = 28

  11. 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. number of laps frequency (x) 1 - 5 2 6 – 10 9 11 – 15 15 16 – 20 20 21 – 25 17 26 – 30 25 31 – 35 2 36 - 40 1 Data is grouped into 8 class intervals of width 4.

  12. 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. number of laps frequency midpoint(c.c) c.c. X f 1 - 5 2 6 – 10 9 11 – 15 15 16 – 20 20 21 – 25 17 26 – 30 25 31 – 35 2 36 - 40 1 3 6 8 72 13 195 18 360 23 391 700 28 66 33 38 38 Mean estimate = 1828/91 = 20.1 laps

  13. 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. number of laps frequency (x) 1 - 5 2 6 – 10 9 11 – 15 15 Modal Class 26 - 30 16 – 20 20 21 – 25 17 26 – 30 25 31 – 35 2 36 - 40 1

  14. 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.  number of laps frequency (x) 1 - 5 2 (91+1)/2 = 46 6 – 10 9 11 – 15 15 16 – 20 20 21 – 25 17 26 – 30 25 31 – 35 2 36 - 40 1 The 46th data value is in the 16 – 20 class , median ≈ 18 c. F. 2 11 26 46 63 88 90 91

More Related