Statistics S 5 Int 2 www mathsrevision com

Statistics S 5 Int 2 www. mathsrevision. com Quartiles from a Frequency Table Quartiles from a Cumulative Frequency Table Estimating Quartiles from C. F Graphs Standard Deviation from a sample Scatter Graphs Probability Relative Frequency & Probability 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 5 Int 2 15 -Sep-20 Created by Mr Lafferty Maths Dept

Statistics Quartiles from Frequency Tables www. mathsrevision. com S 5 Int 2 Learning Intention Success Criteria 1. To explain how to calculate quartiles from frequency tables. 15 -Sep-20 1. Know the term quartiles. 2. Calculate quartiles given a frequency table. Created by Mr Lafferty Maths Dept

Statistics Quartiles from Frequency Tables S 5 Int 2 www. mathsrevision. com Reminder ! Range : The difference between highest and Lowest values. It is a measure of spread. Median : The middle value of a set of data. When they are two middle values the median is half way between them. Mode : The value that occurs the most in a set of data. Can be more than one value. Quartiles : The median splits into lists of equal length. The medians of these two lists are called quartiles. 15 -Sep-20 Created by Mr Lafferty Maths Dept

Statistics Quartiles from Frequency Tables www. mathsrevision. com S 5 Int 2 To find the quartiles of an ordered list you consider its length. You need to find three numbers which break the list into four smaller list of equal length. Example 1 : For a list of 24 numbers, 24 ÷ 6 = 4 6 number Q 1 6 number Q 2 6 number Q 3 The quartiles fall in the gaps between Q 1 : the 6 th and 7 th numbers Q 2 : the 12 th and 13 th numbers Q 3 : the 18 th and 19 th numbers. 15 -Sep-20 Created by Mr Lafferty Maths Dept R 0 6 number

Statistics Quartiles from Frequency Tables www. mathsrevision. com S 5 Int 2 Example 2 : For a list of 25 numbers, 25 ÷ 4 = 6 6 number Q 1 6 number 1 No. 6 number Q 3 6 number Q 2 The quartiles fall in the gaps between Q 1 : the 6 th and 7 th Q 2 : the 13 th Q 3 : the 19 th and 20 th numbers. 15 -Sep-20 Created by Mr Lafferty Maths Dept R 1

Statistics Quartiles from Frequency Tables www. mathsrevision. com S 5 Int 2 Example 3 : For a list of 26 numbers, 26 ÷ 4 = 6 6 number 1 No. 6 number Q 2 6 number Q 1 1 No. Q 3 The quartiles fall in the gaps between Q 1 : the 7 th number Q 2 : the 13 th and 14 th number Q 3 : the 20 th number. 15 -Sep-20 Created by Mr Lafferty Maths Dept R 2 6 number

Statistics Quartiles from Frequency Tables www. mathsrevision. com S 5 Int 2 Example 4 : For a list of 27 numbers, 27 ÷ 4 = 6 6 number 1 No. Q 1 6 number 1 No. 6 number Q 2 1 No. Q 3 The quartiles fall in the gaps between Q 1 : the 7 th number Q 2 : the 14 th number Q 3 : the 21 th number. 15 -Sep-20 Created by Mr Lafferty Maths Dept R 3 6 number

Statistics Quartiles from Frequency Tables www. mathsrevision. com S 5 Int 2 Example 4 : For a ordered list of 34. Describe the quartiles. 34 ÷ 4 = 8 8 number 1 No. 8 number R 2 Q 2 8 number Q 1 15 -Sep-20 1 No. Q 3 The quartiles fall in the gaps between Q 1 : the 9 th number Q 2 : the 17 th and 18 th number Q 3 : the 26 th number. Created by Mr Lafferty Maths Dept 8 number

Statistics Quartiles from Frequency Tables www. mathsrevision. com S 5 Int 2 Now try Exercise 1 Start at 1 b Ch 11 (page 162) 15 -Sep-20 Created by Mr Lafferty Maths Dept

Starter Questions www. mathsrevision. com S 5 Int 2 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Statistics www. mathsrevision. com S 5 Int 2 Quartiles from Cumulative Frequency Table Learning Intention Success Criteria 1. To explain how to calculate quartiles from Cumulative Frequency Table. 15 -Sep-20 1. Find the quartile values from Cumulative Frequency Table. Created by Mr. Lafferty Maths Dept.

Statistics Quartiles from Cumulative Frequency Table S 5 Int 2 www. mathsrevision. com Example 1 : The frequency table shows the length of phone calls ( in minutes) made from an office in one day. 15 -Sep-20 Created by Mr. Lafferty Maths Dept. Time Freq. (f) 1 2 2 2 3 5 10 4 8 18 5 4 22 Cum. Freq.

Statistics www. mathsrevision. com S 5 Int 2 Quartiles from Cumulative Frequency Table We use a combination of quartiles from a frequency table and the Cumulative Frequency Column. For a list of 22 numbers, 22 ÷ 4 = 5 5 number 1 No. 5 number Q 2 5 number Q 1 1 No. R 2 5 number Q 3 The quartiles fall in the gaps between Q 1 : the 6 th number Q 1 : 3 minutes Q 2 : the 11 th and 12 th number Q 2 : 4 minutes Q 3 : the 17 th number. Q 3 : 4 minutes 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Statistics Quartiles from Cumulative Frequency Table S 5 Int 2 www. mathsrevision. com Example 2 : A selection of schools were asked how many 5 th year sections they have. Opposite is a table of the results. No. Of Sections Calculate the quartiles for the results. 15 -Sep-20 Created by Mr. Lafferty Maths Dept. Freq. Cum. Freq. (f) 4 3 3 5 5 8 6 8 16 7 9 25 8 8 33

Statistics www. mathsrevision. com S 5 Int 2 Quartiles from Cumulative Frequency Table We use a combination of quartiles from a frequency table and the Cumulative Frequency Column. Example 2 : For a list of 33 numbers, 33 ÷ 4 = 8 8 number Q 1 8 number 1 No. 8 number Q 3 8 number Q 2 The quartiles fall in the gaps between Q 1 : the 8 th and 9 th numbers Q 1 : 5. 5 Q 2 : the 17 th number Q 2 : 7 Q 3 : the 25 th ad 26 th numbers. Q 3 : 7. 5 15 -Sep-20 Created by Mr. Lafferty Maths Dept. R 1

Statistics www. mathsrevision. com S 5 Int 2 Quartiles from Cumulative Frequency Table Now try Exercise 2 Ch 11 (page 163) 15 -Sep-20 Created by Mr Lafferty Maths Dept

Starter Questions www. mathsrevision. com S 5 Int 2 3 cm 29 o 4 cm A C 70 o 53 o 15 -Sep-20 Created by Mr. Lafferty Maths Dept. B 8 cm

Quartiles from Cumulative Frequency Graphs www. mathsrevision. com S 5 Int 2 Learning Intention Success Criteria 1. To show to estimate quartiles from cumulative frequency graphs. 15 -Sep-20 1. Know the terms quartiles. 2. Estimate quartiles from cumulative frequency graphs. Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com S 5 Int 2 Quartiles from Cumulative Frequency Graphs Number of sockets 10 20 30 40 50 60 Cumulative Frequency 2 9 24 34 39 40

New Term www. mathsrevision. com S 5 Int 2 Cumulative Frequency Interquartile range Graphs range Semi-interquartile (Q 3 – Q 1 )÷ 2 = (36 - 21)÷ 2 =7. 5 Q 3 Q 2 Q 1 Q 3 =36 Q 2 =27 Q 1 =21 Quartiles 40 ÷ 4 =10

www. mathsrevision. com S 5 Int 2 Quartiles from Cumulative Frequency Graphs Km travelled on 1 gallon (mpg) 20 25 30 35 40 45 50 Cumulative Frequency 3 11 30 53 69 76 80

New Term www. mathsrevision. com S 5 Int 2 Cumulative Frequency Interquartile range Graphs range Semi-interquartile (Q 3 – Q 1 )÷ 2 = (37 - 28)÷ 2 =4. 5 Q 3 = 37 Q 2 = 32 Q 1 =28 Quartiles 80 ÷ 4 =20

Quartiles from Cumulative Frequency Graphs www. mathsrevision. com S 5 Int 2 Now try Exercise 3 Ch 11 (page 166) 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 5 Int 2 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Standard Deviation www. mathsrevision. com S 5 Int 2 Learning Intention Success Criteria 1. To explain the term and calculate the Standard Deviation for a collection of data. 15 -Sep-20 1. Know the term Standard Deviation. 1. Calculate the Standard Deviation for a collection of data. Created by Mr. Lafferty Maths Dept.

Standard Deviation For a FULL set of Data www. mathsrevision. com S 5 Int 2 The range measures spread. Unfortunately any big change in either the largest value or smallest score will mean a big change in the range, even though only one number may have changed. The semi-interquartile range is less sensitive to a single number changing but again it is only really based on two of the score. 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Standard Deviation For a FULL set of Data S 5 Int 2 www. mathsrevision. com A measure of spread which uses all the data is the Standard Deviation The deviation of a score is how much the score differs from the mean. 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com S 5 Int 2 Step 25: : Score - Mean Deviation Step 1 : Find. Standard the mean Step 4 : Mean square deviation For a Take FULL set of Data the square root of step 4 375 ÷ 5 = 75 2 Step 3 : (Deviation)68 ÷ 5 = 13. 6 √ 13. 6 deviation = 3. 7 Example 1 : Find the standard of these five scores 70, 72, 75, 78, 80. Standard Deviation is 3. 7 (to 1 d. p. ) Score Deviation (Deviation)2 70 -5 25 72 -3 9 75 0 0 3 9 78 5 25 80 0 68 Totals 375 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

5 Deviation : square deviation Step 1 : Find. Standard the mean Step 4 Step : Mean Step 2 : Score - Mean www. mathsrevision. com S 5 Int 2 For a FULL set of Data 2 Take the square root of step 4 Step 180 3 : ÷(Deviation) 6 = 30 962 ÷ 6 = 160. 33 = 12. 7 (to 1 d. p. ) Example 2 √ 160. 33 : Find the standard deviation of these six amounts of money £ 12, £ 18, £ 27, £ 36, £ 37, £ 50. Standard Deviation is £ 12. 70 Score Deviation (Deviation)2 12 -18 324 18 -12 144 27 -3 9 6 36 36 7 49 37 20 400 50 962 15 -Sep-20 Totals 180 Created by Mr. Lafferty Maths Dept. 0

Standard Deviation For a FULL set of Data www. mathsrevision. com S 5 Int 2 When Standard Deviation is LOW it means the data values are close to the MEAN. When Standard Deviation is HIGH it means the data values are spread out from the MEAN. Mean 15 -Sep-20 Mean Created by Mr. Lafferty Maths Dept.

Standard Deviation www. mathsrevision. com S 5 Int 2 Now try Exercise 4 Ch 11 (page 169) 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 5 Int 2 15 -Sep-20 Waist Sizes Frequency 28” 7 30” 12 32” 23 34” 14 Created by Mr. Lafferty Maths Dept.

Standard Deviation For a Sample of Data www. mathsrevision. com S 5 Int 2 Learning Intention Success Criteria 1. To show to calculate the Standard deviation for a sample of data. 1. Construct a table to calculate the Standard Deviation for a sample of data. 2. Use the table of values to calculate Standard Deviation of a sample of data. 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com S 5 Int 2 Standard Deviation For a Sample of. We Data will use this version because it is easier to use in a sample In real life situations it is normal to work with practice ). ! of data ( survey / questionnaire We can use two formulae to calculate the sample deviation. s = standard deviation x = sample mean 15 -Sep-20 ∑ = The sum of n = number in sample Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com 2: Q 1 a. Calculate the mean : Q 1 a. Step Calculate the Standard Deviation Step 592 1 : ÷ 8 = 74 Step 3 : sample deviation all the values For a Sample. Square of Data S 5 Int 2 find the total Sum all the values. Use formula toand calculate sample have deviation Example 1 a : Eight athletes heart rates 70, 72, 73, 74, 75, 76 and 76. Heart rate (x) 15 -Sep-20 x 2 70 4900 72 5184 73 5329 74 5476 75 5625 76 5776 76 76 5776 Totals ∑x = 592 ∑x 2 = 43842 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com S 5 Int 2 Q 1 b(i) Calculate the mean : Standard Deviation Q 1 b(ii) Calculate the 720 ÷ 8 = 90 sample deviation For a Sample of Data Example 1 b : Eight office staff train as athletes. Their Pulse rates are 80, 81, 83, 90, 94, 96 and 100 BPM Heart rate (x) 15 -Sep-20 x 2 80 6400 81 6561 83 6889 90 8100 94 8836 96 9216 96 100 9216 10000 Totals ∑x = 720 ∑x 2 = 65218 Created by Mr. Lafferty Maths Dept.

Standard Q 1 b(iii) Who. Deviation are fitter Q 1 b(iv) What does the athletes or of staff. Forthe adeviation Sample Data tell us. Compare means Staff data is more spread Athletes are fitter out. www. mathsrevision. com S 5 Int 2 Athletes 15 -Sep-20 Staff Created by Mr. Lafferty Maths Dept.

Standard Deviation For a Sample of Data www. mathsrevision. com S 5 Int 2 Now try Ex 5 & 6 Ch 11 (page 171) 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 5 Int 2 33 o 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Scatter Graphs Construction of Scatter Graphs www. mathsrevision. com S 5 Int 2 Learning Intention 1. To construct and interpret Scattergraphs. Success Criteria 1. Construct and understand the Key-Points of a scattergraph. 2. Know the term positive and negative correlation. 15 -Sep-20 Created by Mr Lafferty Maths Dept

www. mathsrevision. com S 5 Int 2 This scattergraph shows the heights and weights of a sevens football team Write down height and Scatter Graphs weight of each player. Construction of Scatter Graph Bob Tim Sam Joe Gary Jim 15 -Sep-20 Created by Mr Lafferty Maths Dept Dave

Scatter Graphs Construction of Scatter Graph www. mathsrevision. com S 5 Int 2 When two quantities are strongly connected we say there is a strong correlation between them. Best fit line x x x Strong positive correlation 15 -Sep-20 x x x Best fit line Strong negative correlation Created by Mr Lafferty Maths Dept

Scatter Graphs Construction of Scatter Graph www. mathsrevision. com S 5 Int 2 Key steps to: Drawing the best fitting straight line to a scatter graph 1. Plot scatter graph. 2. Calculate mean for each variable and plot the coordinates on the scatter graph. 3. Draw best fitting line, making sure it goes through mean values. 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Find. Mean the mean Age = 2. 9 for the. Age and Prices Mean Price = £ 6000 S 5 Int 2 values. Draw in the best fit line Scatter Graphs www. mathsrevision. com Construction of Scatter Graph Price Age (£ 1000) 1 1 9 8 2 3 3 3 4 4 5 8 7 6 5 5 4 2 15 -Sep-20 St ro ng ne ga t ive co r Is there a correlation? If yes, what kind? re Created by Mr Lafferty Maths Dept lat ion

Scatter Graphs Construction of Scatter Graph www. mathsrevision. com S 5 Int 2 Key steps to: Finding the equation of the straight line. 1. Pick any 2 points of graph ( pick easy ones to work with). 2. Calculate the gradient using : 3. Find were the line crosses y–axis this is b. 4. Write down equation in the form : y = ax + b 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Scatter Graphs Crosses y-axis at 10 www. mathsrevision. com S 5 Int 2 Pick points (0, 10) and (3, 6) y = -1. 33 x + 10 15 -Sep-20 Created by Mr Lafferty Maths Dept

Scatter Graphs Construction of Scatter Graph www. mathsrevision. com S 5 Int 2 Now try Exercise 7 Ch 11 (page 175) 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 5 Int 2 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Probability www. mathsrevision. com S 5 Int 2 Learning Intention 1. To understand probability in terms of the number line and calculate simple probabilities. Success Criteria 1. Understand the probability line. 2. Calculate simply probabilities. 15 -Sep-20 Created by Mr Lafferty Maths Dept

Probability Likelihood Line www. mathsrevision. com S 5 Int 2 0 Impossible Seeing a butterfly In July 15 -Sep-20 0. 5 Not very likely School Holidays Evens Winning the Lottery Created by Mr Lafferty Maths Dept 1 Very likely Baby Born A Boy Certain Go back in time

Probability Likelihood Line www. mathsrevision. com S 5 Int 2 0 Impossible It will Snow in winter 15 -Sep-20 0. 5 Not very likely Evens Homework Everyone getting Every week 100 % in test Created by Mr Lafferty Maths Dept 1 Very likely Certain Toss a coin Going without That land Food Heads for a year.

Probability www. mathsrevision. com S 5 Int 2 We can normally attach a value to the probability of an event happening. To work out a probability P(A) = Probability is ALWAYS in the range 0 to 1 15 -Sep-20 Created by Mr Lafferty Maths Dept

Probability Number Likelihood Line S 5 Int 2 www. mathsrevision. com 1 0 2 0. 1 Impossible 3 0. 2 4 0. 3 5 0. 4 6 0. 5 0. 6 8 7 0. 8 0. 9 Evens Q. What is the chance of picking a number between 1 – 8 ? 1 Certain P= 8 =1 8 4 P(E) = = 0. 5 8 Q. What is the chance of picking the number 1 ? 1 P(1) = = 0. 125 15 -Sep-20 Created by Mr Lafferty Maths Dept 8 Q. What is the chance of picking a number that is even ?

Probability Likelihood Line S 5 Int 2 www. mathsrevision. com 52 cards in a pack of cards 0 0. 1 Impossible 0. 2 0. 3 Not very likely 0. 4 0. 5 Evens 0. 6 0. 7 0. 8 Very likely 0. 9 1 Certain 26 P (Red) = Q. What is the chance of picking a red card ? = 0. 5 52 13 Q. What is the chance of picking a diamond ? P (D) = = 0. 25 52 4 Q. What is the chance of picking ace ? P (Ace) = = 0. 08 52 15 -Sep-20 Created by Mr Lafferty Maths Dept

Probability www. mathsrevision. com S 5 Int 2 Now try Ex 8 Ch 11 (page 177) 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 5 Int 2 15 -Sep-20 Created by Mr Lafferty Maths Dept

Relative Frequencies www. mathsrevision. com S 5 Int 2 Learning Intention Success Criteria 1. To understand the term relative frequency. 1. Know the term relative frequency. 2. Calculate relative frequency from data given. 15 -Sep-20 Created by Mr Lafferty Maths Dept

Relative Frequencies S 5 Int 2 www. mathsrevision. com Relative Frequency always added up to 1 How often an event happens compared to the total number of events. Example : Wine sold in a shop over one week Country Frequency France 180 Italy 90 Spain 90 90 ÷ 360 = Total 360 1 15 -Sep-20 Relative Frequency 180 ÷ 360 = 0. 5 90 ÷ 360 = 0. 25 Created by Mr Lafferty Maths Dept 0. 25

Relative Frequencies S 5 Int 2 www. mathsrevision. com Example Calculate the relative frequency for boys and girls born in the Royal Infirmary hospital in December 2007. Boys Girls Total Frequency 300 200 500 Relative Frequency 0. 6 0. 4 1 15 -Sep-20 Created by Mr Lafferty Maths Dept Relative Frequency adds up to 1

Relative Frequencies www. mathsrevision. com S 5 Int 2 Now try Ex 9 Ch 11 (page 179) 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 5 Int 2 15 -Sep-20 Created by Mr. Lafferty Maths Dept.

Probability from Relative Frequency www. mathsrevision. com S 5 Int 2 Learning Intention 1. To understand the connection of probability and relative frequency. 15 -Sep-20 Success Criteria 1. Know the term relative frequency. 2. Estimate probability from the relative frequency. Created by Mr Lafferty Maths Dept

www. mathsrevision. com S 5 Int 2 When the sum of the Probability from frequencies is LARGE the relative frequency is a good Relative Frequency estimate of the probability of an outcome Example 1 Three students carry out a survey to study left handedness in a school. Results are given below 15 -Sep-20 Number of Left - Hand Students Total Asked Sean 2 10 Karen 3 25 Daniel 20 200 Created by Mr Lafferty Maths Dept Relative Frequency

www. mathsrevision. com S 5 Int 2 Who’s results would you from Probability Megan’s use as a estimate of the Relative Frequency probability of a house being alarmed ? Example Three 2 students carry out a survey to study how many houses had an alarm system in a particular area. What is the Results are given below probability 0. 4 that a house is Number of Relative Total alarmed ? Alarmed Asked Frequency Houses 15 -Sep-20 Paul 7 10 Amy 12 20 Megan 40 100 Created by Mr Lafferty Maths Dept

Probability from Relative Frequency www. mathsrevision. com S 5 Int 2 Now try Ex 10 Ch 11 Start at Q 2 (page 181) 15 -Sep-20 Created by Mr. Lafferty Maths Dept.