Q1: Calculate the mean, median, sample variance, and standard deviation of 25, 40, 05, 70, 05, 40, 70.
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1 Q1: Calculate the mean, medan, sample varance, and standard devaton of 5, 40, 05, 70, 05, 40, 70. Q: The frequenc dstrbuton for a data set s gven below. Measurements Frequenc a) What happens to the mean f we double the frequences? (Now we have 40 data ponts) The mean does not change f the frequences are doubled. In such a case, the sum of the data ponts wll get doubled, and the number of data ponts s doubled also. Therefore rato of the sum of the data ponts to the number of data ponts wll sta the same. b) What happens to the mean f we double the measurement values? (There are stll 0 data ponts) The mean gets doubled. The sum of the data ponts get doubled because ou have doubled each measurement value, but the number of data ponts stas the same, causng the mean to get doubled. c) Does the standard devaton ncrease, decrease, or sta the same f we double the frequences? n The term gets doubled because snce the frequences are doubled, ou have to add the n square of each number twce. The term gets doubled also, as eplaned n part a. When
2 the frequences are doubled, because of the term, the standard devaton decreases ver slghtl. d) What happens to the standard devaton f we double the measurement values? n The term gets multpled b 4, as each value s twce the orgnal value, so ther squares wll be 4 tmes the squares of the orgnal values. The term n gets doubled as eplaned n part b. The varance where the measurement values are NOT doubled s: 0 0 [ ( ) ] The varance where the measurement values ARE doubled s: 0 [ ( ) ], whch s equvalent to 0 [ 0 ( 0 ) ] Therefore the varance s 4 tmes the ntal varance. Snce the standard devaton s the square root of varance, the standard devaton gets doubled. Q3: What s the 85 th percentle of the data set consstng of all natural numbers between 1 and 140? The data set s: { }. There are 140 numbers n the data set. Snce the 85 th percentle s asked, p= Np= 11. The 85 th percentle s gven b. s 11, and s 10. Therefore the answer s Q5: a) The stem-and-leaf dagram of the age of a group of tenns plaers s shown below: Fnd the mode, IQR, and relatve frequenc of 4. b) 37 students receved a hgher grade than Nuran on mdterm 1. whch was taken b 183 students. What s the percentle of Nuran s grade? c) The average weght of a group of 40 Sumo wrestlers s kg, and the medan s 141 kg. What can ou sa about the dstrbuton of weght among ths group? Eplan!
3 Q6: A bvarate numercal data set conssts of the pars of values (-,-3), (-1,-3), (0,-), (1,-), (,-1), (3,0), (4,1) for the varables (,). a) Fnd the correlaton coeffcent b) Fnd the least square ftted lne c) What s the vertcal error E 3 for the thrd pont (0,-)?
4 Q7 The weght and heght of female students was measured. Let 1,..., be the weght measurements, and let 1,..., be the heght measurements. The sample averages are 58 kg and 163 cm, and the sample standard devatons are 6.1 kg and 4.8 cm. The correlaton coeffcent between weght and heght measurements s 0.4 a) Fnd and b) Fnd ( )( ) What s gven n the queston: = 58 = 163 = 6.1 = 4.8 r = 0.4 c) Fnd
5 a) ( ) We know that s 6.1, and that the sum of the values of (the sum of the weghts) s the average of the weghts tmes the number of people. can easl be calculated. ( ( = Smlarl, ( ( ( ) ) ) ) ) = b) ( )( ), so we can fnd b fndng and. (r s alread known to be 0.4). We can fnd and snce and. and Therefore,
6 c) = Q: The number of goals scored per game b Lverpool at Anfeld Road n the last three seasons s gven b the followng table: Goals per game Frequenc A 0 1 Rel. Freq a) What s A? What s the relatve frequenc of 3 goals scored per game? b) Do a Boplot of the data. (If ou could not fnd A n part (a), assume ts 0) Q10: There are three -3 s, four -1 s, two 0 s, four s, and one 3 n a data set of temperatures (n degrees Celsus). a) Draw a relatve frequenc hstogram
7 b) Fnd the mode, medan, mean, and 70 th percentle. Mode = -1 and Medan = = 70 th percentle: p= 0.7 Np=.8 k=10 The 70 th percentle s equal to, whch s. c) Repeat (b) after addng two -3 s and two 3 s to the temperature data set. The mode becomes -3, snce there are more -3 s than anthng else now. d) Repeat (b) after convertng the temperature data n Celsus to a temperature data n Fahrenhet. ( Degrees Fahrenhet = 1.8 Degrees Celsus + 3. Eample: 41 F 5 C )
8 Q11: 0 data ponts, some sums and the correlalaton coeffcent are gven below. X j1 56, 0 110, , 0 665, 0 A, r (a) What s the value of S? (b) What does r = tell ou? Eplan. (c) What s A (the sum of the cross products of the and )? (d) Fnd the mean and standard devaton for the, and the mean for the.
9 Q1: There are 5 data ponts, (, ), = 1,...,5. Also, 30 and. The ftted least squares lne (regresson lne) of the data set s ˆ (a) Fnd S. (b) Fnd S. (c) Fnd. 5
10 Q 13: The hstogram of a dscrete data set consstng of 100 measurements s gven below. Hstogram Relatve Frequenc 0,4 0,3 0, 0,1 0 0,35 0,5 0,15 0,15 0,1 1, 3,3 5, 6,3 (a) Fnd the mode, medan and mean. (b) Fnd the nterquartle range. (c) Fnd the frequenc of. (d) Fnd the sum of data ponts. N (e) The varance s.687. What s?
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