ࡱ> y`  /bjbjss q%e%   8ʙ~ ~b"b d d d d d d $h  L 1  b b 0  r Uo$t 0 O&H   ud  Vc6 c  MATHEMATICS WORKSHEET XI Grade (Semester 1) Chapter 1  Worksheet 7th  Topic : Median, Quartiles, and Percentiles TIME : 3 X 45 minutes  SMAK ST. ALBERTUS (ST. ALBERT Senior High School) Talang 1 Street Malang 65112, Indonesia Phone (0341) 564556, 581037 Fax.(0341) 552017 Email:  HYPERLINK "mailto:sma@dempoku.com" sma@dempoku.com homepage: http://www.dempo.org STANDARD COMPETENCY : To use the rules of statistics, the rules of counting, and the properties of probability in problem solving. BASIC COMPETENCY: To calculate the centre of measurement, the location of measurement, and the dispersion of measurement from the grouped data, altogether with their interpretations. In this chapter, you will learn: How to calculate the median and quartiles of grouped data. How to estimate the median and quartiles from the cumulative frequency curve. The Median, Quartile, and Percentile of grouped data By Ogive ( We recall that the median (=Q2) is the middle value when a set of data is arranged in order of increasing magnitude.   Q1 = the lower quartile Q2 = median Q3 = the upper quartile We can estimate Q1, Q2, Q3 from the cumulative frequency and calculate them with the formula. Median corresponds to the 50th percentile, Q1 corresponds to the 25th percentile, Q3 corresponds to the 75th, i.e. Q2 = P50 , Q1 = P25 , Q3 = P75 . By Formula ( The Median   EMBED Equation.3   EMBED Equation.3  = median  EMBED Equation.3 = the lower boundary of median  EMBED Equation.3  = the sum of data  EMBED Equation.3  = the cumulative frequency before the median class  EMBED Equation.3  = the frequency of the median class  EMBED Equation.3  = the width of interval class The Lower Quartile   EMBED Equation.3   EMBED Equation.3  = the lower quartile  EMBED Equation.3 = the lower boundary of the lower quartile  EMBED Equation.3  = the sum of data  EMBED Equation.3  = the cumulative frequency before the lower quartile class  EMBED Equation.3  = the frequency of the lower quartile class  EMBED Equation.3  = the width of interval class The Upper Quartile   EMBED Equation.3   EMBED Equation.3  = the upper quartile  EMBED Equation.3 = the lower boundary of the upper quartile  EMBED Equation.3  = the sum of data  EMBED Equation.3  = the cumulative frequency before the upper quartile class  EMBED Equation.3  = the frequency of the upper quartile class  EMBED Equation.3  = the width of interval class The Percentile   EMBED Equation.3   EMBED Equation.3  = the  EMBED Equation.3 th percentile  EMBED Equation.3 = the lower boundary of the  EMBED Equation.3 th percentile  EMBED Equation.3  = the sum of data  EMBED Equation.3  = the cumulative frequency before the  EMBED Equation.3 th percentile class  EMBED Equation.3  = the frequency of the  EMBED Equation.3 th percentile class  EMBED Equation.3  = the width of interval class The Limit of  EMBED Equation.3    EMBED Equation.3  Example 37 The length of 40 insects of a certain species were measured correct to the nearest millimeter. Lengths (mm)Frequency ( EMBED Equation.3 )Use the cumulative frequency curve (ogive) to estimate: the median length the upper quartile the lower quartile 25 29230 34435 39 740 441045 49850 54655 593 Solution The cumulative frequency table is constructed below. The table shows the cumulative frequency distribution of the length of 40 insects.  the median length, 50% of the total frequency =  EMBED Equation.3  From the curve, the median length = the upper quartile, 75% of the total frequency =  EMBED Equation.3  From the curve, the upper quartile = the lower quartile, 25% of the total frequency =  EMBED Equation.3  From the curve, the lower quartile = By formula: Lengths (mm)Frequency ( EMBED Equation.3 )The cumulative frequency 25 292230 34435 39 740 441045 49850 54655 593 n = x 40 = 20, 20 in the class 40 44 .  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  n = x = , in the class  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  n = x = , in the class  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Example 38  The examination marks of 100 pupils are given in the table: Construct a cumulative frequency table, using the classes  EMBED Equation.3 , EMBED Equation.3 , and so on. Draw the cumulative frequency curve for the result obtained. Use your curve to estimate and the formula to calculate the median mark the upper quartile the lower quartile the minimum mark required to gain a distinction if the top 5% of the pupils are awarded a distinctionMark Number of pupils EMBED Equation.3 2 EMBED Equation.3 12 EMBED Equation.3 25 EMBED Equation.3 29 EMBED Equation.3 15 EMBED Equation.3 10 EMBED Equation.3 4 EMBED Equation.3 3  Solution The table below shows the cumulative frequency table. Mark Number of pupils EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  b. The graph below shows the cumulative frequency curve for the results:  c. By formula Q2 = Q3 = Q1 = X95 =  Exercise 7 In an agricultural experiment, the lengths of 124 ears of barley were measured. The data obtained is expressed in the following table: Length (mm)Number of ears of barley EMBED Equation.3 1 EMBED Equation.3 8 EMBED Equation.3 35 EMBED Equation.3 50 EMBED Equation.3 25 EMBED Equation.3 5 Construct a cumulative frequency table, using the classes 20 or less, 30 or less, and so on Draw the cumulative frequency curve for the results. Use your graph to estimate the median. Use the formula to calculate the median. From the graph find the number of ears of barley with lengths greater that 55 mm, either not greater than 25 mm or greater than 64 mm. It was discovered later than all the lengths were wrongly recorded such that all lengths should be 5 mm more. Find the correct value of the median. The table below shows the distribution of the marks scored by 600 pupils in an examination: Marks 10 20 30 40 50 60 708090100Number of pupils scoring less than this mark92788180308415497568590600 Using a vertical scale of 1 cm for 50 pupils and a horizontal scale of 1 cm for 10 marks, plot these values and draw a smooth curve through your plotted points. Use your graph to estimate the median mark, the pass mark such that 60% of the pupils will pass the examination. Indicate clearly the upper and the lower quartile on your graph. Use the formula to calculate the upper and the lower quartile. 64 adults were asked to indicate the weekly number of hours they spend watching television. The table below shows the information obtained: Length (mm)Number of worms EMBED Equation.3 2 EMBED Equation.3 8 EMBED Equation.3 22 EMBED Equation.3 16 EMBED Equation.3 10 EMBED Equation.3 4 EMBED Equation.3 2Copy and complete the cumulative frequency table below: Time (h) EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 Number of adults02080260500580600 Using a vertical scale of 2 cm to represent 10 adults and a horizontal scale of 2 cm to represent 5 hours, draw a cumulative frequency curve to display the information. Use your graph to estimate the median, the upper and the lower quartile, the number of adults who spend more than 25 hours per week watching television. The results of 56 students in an examination are tabulated below: Mark ( EMBED Equation.3 )Frequency EMBED Equation.3 1 EMBED Equation.3 3 EMBED Equation.3 4 EMBED Equation.3 5 EMBED Equation.3 7 EMBED Equation.3 8 EMBED Equation.3 11 EMBED Equation.3 9 EMBED Equation.3 6 EMBED Equation.3 2 Using the formula, calculate the median, the lower quartile, and the upper quartile. Calculate the percentage of students who scored a mark greater than or equal to 65, less than 34 The table below shows the distribution of marks scored by 500 cadets in a physical test: Calculate the mean work. Construct the cumulative frequency table. Draw a cumulative frequency curve representing the distribution. Estimate from the graph and calculate by the formula: the median, the 70th percentile, the upper and the lower quartile, the number of cadets who scored less than 43 marks, the pass mark given that 60% of the cadets passed the physical test.Mark ( EMBED Equation.3 )Number of cadets  EMBED Equation.3 9 EMBED Equation.3 17 EMBED Equation.3 63 EMBED Equation.3 65 EMBED Equation.3 86 EMBED Equation.3 112 EMBED Equation.3 68 EMBED Equation.3 55 EMBED Equation.3 17 EMBED Equation.3 8  Adapted from New Syllabu s Mathematics 4, Teh Keng Seng BSc, Dip Ed & Looi Chin Keong BSc. 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