good day tutor , this is my grouped data

please help me find

1 ) ogive

2 ) Central tendency ( Min , Mod , Median )

3 ) Measures of Position ( Quartile )

8) The following data represent the age distribution of a sample of 70 women having multiple- delivery births in 2002. Age Number 15 - 19 20 - 24 5 25 - 29 16 30 - 34 28 35 - 39 17 40 - 44 3Measure of Central Tendency for Grouped Data TEg: Class Mean Frequency (f) Mid-point (x) fx interval Each class interval is represented by 24 - 26 2 25 50 the mid-point of the interval, x 26 -28 4 27 108 28 -30 5 29 145 Find mean by using this formula: 30 -32 2 31 62 Total 1=13 [A= 365 Efx X = Efx 365 n X = 28.0769 n 13Median Eg To find median, create a column for the CF and Class interval Frequency (f) CF P.O.D Position of Data (P.O.D) 23.5 -26.5 2 2 1-2 Determine the Position of Median (P.O.M) 26.5 - 29.5 5 7 3-7 P.O.M = 29.5 - 32.5 3 10 8-10 2 32.5 -35.5 2 12 11-12 Find median by using this formula: Total n=12 Median = Lin + P.O.M - fm-1 x c P.O.M _ n_ 12 fm : 6 2 2 where Lm = lower boundary of the median class Median = Lm+ P.O.M - fm-1 x C= 26.5+ 6-2 x3=28.9 S fm = CF before the median class fm = frequency of the median class c= median class size By using ogive: Previous Eg: 14 12 10 P.O.M = 6 N 0 23.5 26.5 29.5 32.5 35.5 Median = 28.9Mode Eg: Class interval Frequency (f) To find mode, select class with the highest 23.5 -26.5 2 frequency 26.5 - 29.5 5 Find mode by using this formula: 29.5 - 32.5 3 32.5-35.5 2 Mode= L+ fo - fi x c (fo - fi )+ ( fo - f2) Mode= L+ fo - fi X C (fo - fi ) + ( fo - f2) Where 5-2 = 26.5+ (5-2) +(5-3) x 3 L = LB of class containing mode fo = f of the class containing mode = 28.3 f = f of the class before the class containing mode f, = f of the class after the class containing mode c= class size By using histogram: Select the highest bar 6 N class interval Mode9 Measure of PositionEg Third Quartile (Q3) Class interval Frequency (f) CF P.O.D To find Q3, create a column for the CF and Position 23.5- 26.5 2 2 1-2 of Data (P.O.D) 26.5 - 29.5 5 7 3-7 Determine the Position of Q3 (P.O. Q3) 29.5 - 32.5 3 10 8-10 P.O.Q = P.O.Q x 3 32.5- 35.5 2 12 11-12 Find Q3 by using this formula: Total n=12 P.O.Q3 = P.O.Q x 3 = 3x 3 = 9 23 = 12+ P.O.Q3 - fm-1 x C3 f3 Q3 = L3 + P.O.Q3 - fm-1 x cq = 29.5+ 9-7 x3=31.5 where Ly = lower boundary of the Q, class f3 fm-1 = CF before the Q, class f3= frequency of the Q, class C 3= Q, class size By using ogive: Previous Eg: 14 12 10 P.O.Q =9 8 6 4 P.O.Q, = 3 2 0 23.5 26.5 29.5 32.5 35.5 Q1 = 27.1 Q3 = 31.5Measure of Position for Grouped Data First Quartile (Q1) Class interval Frequency (f) CF P.O.D To find Q1, create a column for the CF and Position 23.5 - 26.5 2 2 1-2 of Data (P.O.D) 26.5 - 29.5 5 7 3-7 Determine the Position of Q, (P.O. Q,) 29.5 - 32.5 3 10 8-10 P.O.Q = 32.5- 35.5 2 12 11-12 Total n=12 Find Q, by using this formula: P.O.QE n 12 = 3 4 4 Q = L+ P.0.Q - fm-1 x q Q= 4+| P.0.9 - find x a - 26.5+(3-2 )x3-27.1 (where Ly = lower boundary of the Q, class fix1 = CF before the Q, class f, = frequency of the Q class c,=Q class size Eg: Third Quartile (Q3) Class interval Frequency (f) CF P.O.D To find Q3, create a column for the CF and Position 23.5 - 26.5 2 2 1-2 of Data (P.O.D) 26.5 - 29.5 5 7 3-7 Determine the Position of Q3 (P.O. Q2) 29.5 - 32.5 3 10 8-10 P.O.Q = P.O.Q x 3 32.5 -35.5 2 12 11-12 Find Q; by using this formula: Total 1=12 P.O.Q3 = P.O.Q x 3 = 3x 3 = 9 23 = 12+ P.O.Q3 - fm-1 x C3 f3 Q3 = Lg + P.O.Q3 - fm-1 x c3 = 29.5+ 9-7 x3=31.5 where Ly= lower boundary of the Q, class f3 fm-1 = CF before the Q, class f;= frequency of the Q, class C3= Q, class sizeThe range is the difference between the largesr and the smallest value in a set of data Range = largest value smallestvalue Range = US LB A simple measure of dispersion : 35'5 _ 23'5 =1 2 It measure the total spread of the data a Range is really inuenced by the extreme valuesjn'z ! H J Eg: Find the range for the following data. Range for Grouped Data 12.5, 23.2, 51.1, 14.6, 33.3, 42.5 The range is the difference between the UB of Sol ution: Range = largest value smallest value =511125 \"gjf' =3as the highest class and the LB of the lowest class Range: UB- LB Interquartile Range Semi-interquartile Range / Quartile Deviation The difference between the third and first quartiles in a set of data Semi-interquartile range = Interquartile range / 2 Interquartile range = Q3 - Q Eg : Find the semi-interquartile range This measure the spread in the middle 50% of the Semi-interquartile range data = Interquartile range / 2 =10.5/ 2 It is not influenced by the extreme values =5.25 Eg : The weight (kg) for 20 students are 66, 54, 48, 52, 67, 42, 44, 56, 63, 60, 51, 49, 50, 54, 53, 60, 48, 59, 54 and 50. Find the interquartile range. Q1 =49.25, Q3 = 59.75 Interquartile range = Q3 - Q1 =59.75 - 49.25 =10.52 distribution (A and B) may have the same central locations (mean, median or mode) but different dispersions or spreads If the data are widely dispersed, the central location is said to be less representative of the whole data The more spread out or dispersed the data, the larger is the measures of dispersion If the data is more concentrated, the measures of dispersion is smaller If the data are the same, the measures of dispersion will be zero Therefore, these measures of dispersion are always give positive values Mean Deviation / Average Absolute Deviation Eg: Given 45, 66, 53, 21, 66. Find the mean deviation. 45+ 66+53+ 21+ 66 Mean= = 50.2 5 Mean deviation = Ex- mean n Mean deviation Elx- mean where x= the observation n 45- 50.2 + 66-50.2 + 53-50.2+ 21-50.2 + 66-50.2 n = the number of observation = 5 = 12.56Pearson Coefficient of Skewness x- mode 3( x - median Skewness = or Skewness = S S skewness = 0, symmetrical skewness = +ve value, skewed to the right or positively skewed skewness = -ve value, skewed to the left or negatively skewed